AP Physics 1: Oscillations Multiple-Choice Practice Questions

Test information.

Question

See All test questions

  • » Do AP Physics 1 Practice Tests
  • » Download AP Physics 1 Practice Tests
  • » Best AP Physics 1 Books

More AP Tests

  • AP Physics 1 Practice Test 1
  • AP Physics 1 Practice Test 2
  • AP Physics 1 Practice Test 3
  • AP Physics 1 Practice Test 4
  • AP Physics 1 Practice Test 5
  • AP Physics 1 Practice Test 6
  • AP Physics 1 Practice Test 7
  • AP Physics 1 Practice Test 8
  • AP Physics 1 Practice Test 9
  • AP Physics 1 Practice Test 10
  • AP Physics 1 Practice Test 11
  • AP Physics 1 Practice Test 12
  • AP Physics 1 Practice Test 13
  • AP Physics 1 Practice Test 14
  • AP Physics 1 Practice Test 15
  • AP Physics 1 Practice Test 16
  • AP Physics 1 Practice Test 17
  • AP Physics 1 Practice Test 18
  • AP Physics 1: Vectors Practice Questions
  • AP Physics 1: Kinematics Practice Questions
  • AP Physics 1: Newton's Laws Practice Questions
  • AP Physics 1: Work, Energy, and Power Practice Questions
  • AP Physics 1: Linear Momentum Practice Questions
  • AP Physics 1: Uniform Circular Motion, Newton's Law of Gravitation, and Rotational Motion Practice Questions
  • AP Physics 1: Oscillations Practice Questions
  • AP Physics 1: Waves Practice Questions
  • AP Physics 1: Electric Forces and Fields Practice Questions
  • AP Physics 1: Direct Current Circuits Practice Questions
  • AP Physics 1 Practice Test 19
  • AP Physics 1 Practice Test 20
  • AP Physics 1 Practice Test 21
  • AP Physics 1 Practice Test 22
  • AP Physics 1 Practice Test 23
  • AP Physics 1 Practice Test 24
  • AP Physics 1 Practice Test 25
  • AP Physics 1 Practice Test 26
  • AP Physics 1 Practice Test 27
  • AP Physics 1 Practice Test 28
  • AP Physics 1 Practice Test 29
  • AP Physics 1 Practice Test 30
  • AP Physics 1 Practice Test 31
  • AP Physics 1 Practice Test 32
  • AP Physics 1 Practice Test 33
  • AP Physics 1 Practice Test 34
  • AP Physics 1 Practice Test 35
  • AP Physics 1 Practice Test 36

1. A block attached to an ideal spring undergoes simple harmonic motion. The acceleration of the block has its maximum magnitude at the point where

physics practice problems oscillation

3. A student measures the maximum speed of a block undergoing simple harmonic oscillations of amplitude A on the end of an ideal spring. If the block is replaced by one with twice its mass but the amplitude of its oscillations remains the same, then the maximum speed of the block will

physics practice problems oscillation

4. A spring-block simple harmonic oscillator is set up so that the oscillations are vertical. The period of the motion is T . If the spring and block are taken to the surface of the Moon, where the gravitational acceleration is 1/6 of its value here, then the vertical oscillations will have a period of

physics practice problems oscillation

5. A linear spring of force constant k is used in a physics lab experiment. A block of mass m is attached to the spring and the resulting frequency, f , of the simple harmonic oscillations is measured. Blocks of various masses are used in different trials, and in each case, the corresponding frequency is measured and recorded. If f 2 is plotted versus 1/ m , the graph will be a straight line with slope

physics practice problems oscillation

6. A simple pendulum swings about the vertical equilibrium position with a maximum angular displacement of 5° and period T. If the same pendulum is given a maximum angular displacement of 10°, then which of the following best gives the period of the oscillations?

physics practice problems oscillation

7. A block with a mass of 20 kg is attached to a spring with a force constant k = 50 N/m. What is the magnitude of the acceleration of the block when the spring is stretched 4 m from its equilibrium position?

8. A block with a mass of 10 kg connected to a spring oscillates back and forth with an amplitude of 2 m. What is the approximate period of the block if it has a speed of 4 m/s when it passes through its equilibrium point?

9. A block with a mass of 4 kg is attached to a spring on the wall that oscillates back and forth with a frequency of 4 Hz and an amplitude of 3 m. What would the frequency be if the block were replaced by one with one-fourth the mass and the amplitude of the block is increased to 9 m ?

Simple Harmonic Oscillator

  • Write something.
  • Write something else.
  • Write something different.
  • Write something completely different.
  • acceleration
  • elastic potential energy
  • kinetic energy
  • the total energy of the object-spring system?
  • the kinetic energy of the object?
  • the potential energy of the spring?
  • Determine the spring constant.
  • After 27 periods, the cube comes to rest. Determine the energy dissipated by friction.

  • the number of oscillations of the Human Slingshot (it is not a whole number)
  • the time for the number of oscillations stated above
  • the mass of the passenger
  • the maximum displacement of the passenger from the equilibrium point
  • the spring constant of the two bungee cords combined
  • the maximum pulling force exerted by the ATV
  • the maximum acceleration of the passenger
  • the work done by the ATV
  • the maximum speed of the passenger
  • the period of oscillation
  • the maximum speed

statistical

  • the spring constant ( k ) of this spring
  • the period of the spring if a 4.896 kg mass was attached to the bottom
  • inertial-balance-calibration.txt Derive an equation that relates mass to period for this inertial balance using the measurements taken in the first half of the experiment.
  • inertial-balance-unknowns.txt Apply the equation you just derived to the measurements taken in the second half of this experiment and determine the masses of the objects that the students brought with them to lab.
  • the mass of the empty balance (the mass of the small lab cart) and…
  • the spring constant of the two springs. (Be careful with the units here. The masses were recorded in grams, but the spring constant should be stated in N/m and the newton is based on the kilogram.)
  • 15.1 Simple Harmonic Motion
  • Introduction
  • 1.1 The Scope and Scale of Physics
  • 1.2 Units and Standards
  • 1.3 Unit Conversion
  • 1.4 Dimensional Analysis
  • 1.5 Estimates and Fermi Calculations
  • 1.6 Significant Figures
  • 1.7 Solving Problems in Physics
  • Key Equations
  • Conceptual Questions
  • Additional Problems
  • Challenge Problems
  • 2.1 Scalars and Vectors
  • 2.2 Coordinate Systems and Components of a Vector
  • 2.3 Algebra of Vectors
  • 2.4 Products of Vectors
  • 3.1 Position, Displacement, and Average Velocity
  • 3.2 Instantaneous Velocity and Speed
  • 3.3 Average and Instantaneous Acceleration
  • 3.4 Motion with Constant Acceleration
  • 3.5 Free Fall
  • 3.6 Finding Velocity and Displacement from Acceleration
  • 4.1 Displacement and Velocity Vectors
  • 4.2 Acceleration Vector
  • 4.3 Projectile Motion
  • 4.4 Uniform Circular Motion
  • 4.5 Relative Motion in One and Two Dimensions
  • 5.2 Newton's First Law
  • 5.3 Newton's Second Law
  • 5.4 Mass and Weight
  • 5.5 Newton’s Third Law
  • 5.6 Common Forces
  • 5.7 Drawing Free-Body Diagrams
  • 6.1 Solving Problems with Newton’s Laws
  • 6.2 Friction
  • 6.3 Centripetal Force
  • 6.4 Drag Force and Terminal Speed
  • 7.2 Kinetic Energy
  • 7.3 Work-Energy Theorem
  • 8.1 Potential Energy of a System
  • 8.2 Conservative and Non-Conservative Forces
  • 8.3 Conservation of Energy
  • 8.4 Potential Energy Diagrams and Stability
  • 8.5 Sources of Energy
  • 9.1 Linear Momentum
  • 9.2 Impulse and Collisions
  • 9.3 Conservation of Linear Momentum
  • 9.4 Types of Collisions
  • 9.5 Collisions in Multiple Dimensions
  • 9.6 Center of Mass
  • 9.7 Rocket Propulsion
  • 10.1 Rotational Variables
  • 10.2 Rotation with Constant Angular Acceleration
  • 10.3 Relating Angular and Translational Quantities
  • 10.4 Moment of Inertia and Rotational Kinetic Energy
  • 10.5 Calculating Moments of Inertia
  • 10.6 Torque
  • 10.7 Newton’s Second Law for Rotation
  • 10.8 Work and Power for Rotational Motion
  • 11.1 Rolling Motion
  • 11.2 Angular Momentum
  • 11.3 Conservation of Angular Momentum
  • 11.4 Precession of a Gyroscope
  • 12.1 Conditions for Static Equilibrium
  • 12.2 Examples of Static Equilibrium
  • 12.3 Stress, Strain, and Elastic Modulus
  • 12.4 Elasticity and Plasticity
  • 13.1 Newton's Law of Universal Gravitation
  • 13.2 Gravitation Near Earth's Surface
  • 13.3 Gravitational Potential Energy and Total Energy
  • 13.4 Satellite Orbits and Energy
  • 13.5 Kepler's Laws of Planetary Motion
  • 13.6 Tidal Forces
  • 13.7 Einstein's Theory of Gravity
  • 14.1 Fluids, Density, and Pressure
  • 14.2 Measuring Pressure
  • 14.3 Pascal's Principle and Hydraulics
  • 14.4 Archimedes’ Principle and Buoyancy
  • 14.5 Fluid Dynamics
  • 14.6 Bernoulli’s Equation
  • 14.7 Viscosity and Turbulence
  • 15.2 Energy in Simple Harmonic Motion
  • 15.3 Comparing Simple Harmonic Motion and Circular Motion
  • 15.4 Pendulums
  • 15.5 Damped Oscillations
  • 15.6 Forced Oscillations
  • 16.1 Traveling Waves
  • 16.2 Mathematics of Waves
  • 16.3 Wave Speed on a Stretched String
  • 16.4 Energy and Power of a Wave
  • 16.5 Interference of Waves
  • 16.6 Standing Waves and Resonance
  • 17.1 Sound Waves
  • 17.2 Speed of Sound
  • 17.3 Sound Intensity
  • 17.4 Normal Modes of a Standing Sound Wave
  • 17.5 Sources of Musical Sound
  • 17.7 The Doppler Effect
  • 17.8 Shock Waves
  • B | Conversion Factors
  • C | Fundamental Constants
  • D | Astronomical Data
  • E | Mathematical Formulas
  • F | Chemistry
  • G | The Greek Alphabet

Learning Objectives

By the end of this section, you will be able to:

  • Define the terms period and frequency
  • List the characteristics of simple harmonic motion
  • Explain the concept of phase shift
  • Write the equations of motion for the system of a mass and spring undergoing simple harmonic motion
  • Describe the motion of a mass oscillating on a vertical spring

When you pluck a guitar string, the resulting sound has a steady tone and lasts a long time ( Figure 15.2 ). The string vibrates around an equilibrium position, and one oscillation is completed when the string starts from the initial position, travels to one of the extreme positions, then to the other extreme position, and returns to its initial position. We define periodic motion to be any motion that repeats itself at regular time intervals, such as exhibited by the guitar string or by a child swinging on a swing. In this section, we study the basic characteristics of oscillations and their mathematical description.

Period and Frequency in Oscillations

In the absence of friction, the time to complete one oscillation remains constant and is called the period ( T ) . Its units are usually seconds, but may be any convenient unit of time. The word ‘period’ refers to the time for some event whether repetitive or not, but in this chapter, we shall deal primarily in periodic motion, which is by definition repetitive.

A concept closely related to period is the frequency of an event. Frequency ( f ) is defined to be the number of events per unit time. For periodic motion, frequency is the number of oscillations per unit time. The relationship between frequency and period is

The SI unit for frequency is the hertz (Hz) and is defined as one cycle per second :

A cycle is one complete oscillation .

Example 15.1

Determining the frequency of medical ultrasound.

Solve to find

Significance

Characteristics of simple harmonic motion.

A very common type of periodic motion is called simple harmonic motion (SHM) . A system that oscillates with SHM is called a simple harmonic oscillator .

Simple Harmonic Motion

In simple harmonic motion, the acceleration of the system, and therefore the net force, is proportional to the displacement and acts in the opposite direction of the displacement.

A good example of SHM is an object with mass m attached to a spring on a frictionless surface, as shown in Figure 15.3 . The object oscillates around the equilibrium position, and the net force on the object is equal to the force provided by the spring. This force obeys Hooke’s law F s = − k x , F s = − k x , as discussed in a previous chapter.

If the net force can be described by Hooke’s law and there is no damping (slowing down due to friction or other nonconservative forces), then a simple harmonic oscillator oscillates with equal displacement on either side of the equilibrium position, as shown for an object on a spring in Figure 15.3 . The maximum displacement from equilibrium is called the amplitude ( A ) . The units for amplitude and displacement are the same but depend on the type of oscillation. For the object on the spring, the units of amplitude and displacement are meters.

What is so significant about SHM? For one thing, the period T and frequency f of a simple harmonic oscillator are independent of amplitude. The string of a guitar, for example, oscillates with the same frequency whether plucked gently or hard.

Two important factors do affect the period of a simple harmonic oscillator. The period is related to how stiff the system is. A very stiff object has a large force constant ( k ) , which causes the system to have a smaller period. For example, you can adjust a diving board’s stiffness—the stiffer it is, the faster it vibrates, and the shorter its period. Period also depends on the mass of the oscillating system. The more massive the system is, the longer the period. For example, a heavy person on a diving board bounces up and down more slowly than a light one. In fact, the mass m and the force constant k are the only factors that affect the period and frequency of SHM. To derive an equation for the period and the frequency, we must first define and analyze the equations of motion. Note that the force constant is sometimes referred to as the spring constant .

Equations of SHM

Consider a block attached to a spring on a frictionless table ( Figure 15.4 ). The equilibrium position (the position where the spring is neither stretched nor compressed) is marked as x = 0 x = 0 . At the equilibrium position, the net force is zero.

Work is done on the block to pull it out to a position of x = + A , x = + A , and it is then released from rest. The maximum x -position ( A ) is called the amplitude of the motion. The block begins to oscillate in SHM between x = + A x = + A and x = − A , x = − A , where A is the amplitude of the motion and T is the period of the oscillation. The period is the time for one oscillation. Figure 15.5 shows the motion of the block as it completes one and a half oscillations after release. Figure 15.6 shows a plot of the position of the block versus time. When the position is plotted versus time, it is clear that the data can be modeled by a cosine function with an amplitude A and a period T . The cosine function cos θ cos θ repeats every multiple of 2 π , 2 π , whereas the motion of the block repeats every period T . However, the function cos ( 2 π T t ) cos ( 2 π T t ) repeats every integer multiple of the period. The maximum of the cosine function is one, so it is necessary to multiply the cosine function by the amplitude A .

Recall from the chapter on rotation that the angular frequency equals ω = d θ d t ω = d θ d t . In this case, the period is constant, so the angular frequency is defined as 2 π 2 π divided by the period, ω = 2 π T ω = 2 π T .

The equation for the position as a function of time x ( t ) = A cos ( ω t ) x ( t ) = A cos ( ω t ) is good for modeling data, where the position of the block at the initial time t = 0.00 s t = 0.00 s is at the amplitude A and the initial velocity is zero. Often when taking experimental data, the position of the mass at the initial time t = 0.00 s t = 0.00 s is not equal to the amplitude and the initial velocity is not zero. Consider 10 seconds of data collected by a student in lab, shown in Figure 15.7 .

The data in Figure 15.7 can still be modeled with a periodic function, like a cosine function, but the function is shifted to the right. This shift is known as a phase shift and is usually represented by the Greek letter phi ( ϕ ) ( ϕ ) . The equation of the position as a function of time for a block on a spring becomes

This is the generalized equation for SHM where t is the time measured in seconds, ω ω is the angular frequency with units of inverse seconds, A is the amplitude measured in meters or centimeters, and ϕ ϕ is the phase shift measured in radians ( Figure 15.8 ). It should be noted that because sine and cosine functions differ only by a phase shift, this motion could be modeled using either the cosine or sine function.

The velocity of the mass on a spring, oscillating in SHM, can be found by taking the derivative of the position equation:

Because the sine function oscillates between –1 and +1, the maximum velocity is the amplitude times the angular frequency, v max = A ω v max = A ω . The maximum velocity occurs at the equilibrium position ( x = 0 ) ( x = 0 ) when the mass is moving toward x = + A x = + A . The maximum velocity in the negative direction is attained at the equilibrium position ( x = 0 ) ( x = 0 ) when the mass is moving toward x = − A x = − A and is equal to − v max − v max .

The acceleration of the mass on the spring can be found by taking the time derivative of the velocity:

The maximum acceleration is a max = A ω 2 a max = A ω 2 . The maximum acceleration occurs at the position ( x = − A ) ( x = − A ) , and the acceleration at the position ( x = − A ) ( x = − A ) and is equal to a max a max .

Summary of Equations of Motion for SHM

In summary, the oscillatory motion of a block on a spring can be modeled with the following equations of motion:

Here, A is the amplitude of the motion, T is the period, ϕ ϕ is the phase shift, and ω = 2 π T = 2 π f ω = 2 π T = 2 π f is the angular frequency of the motion of the block.

Example 15.2

Determining the equations of motion for a block and a spring.

Work is done on the block, pulling it out to x = + 0.02 m . x = + 0.02 m . The block is released from rest and oscillates between x = + 0.02 m x = + 0.02 m and x = −0.02 m . x = −0.02 m . The period of the motion is 1.57 s. Determine the equations of motion.

All that is left is to fill in the equations of motion:

The Period and Frequency of a Mass on a Spring

One interesting characteristic of the SHM of an object attached to a spring is that the angular frequency, and therefore the period and frequency of the motion, depend on only the mass and the force constant, and not on other factors such as the amplitude of the motion. We can use the equations of motion and Newton’s second law ( F → net = m a → ) ( F → net = m a → ) to find equations for the angular frequency, frequency, and period.

Consider the block on a spring on a frictionless surface. There are three forces on the mass: the weight, the normal force, and the force due to the spring. The only two forces that act perpendicular to the surface are the weight and the normal force, which have equal magnitudes and opposite directions, and thus sum to zero. The only force that acts parallel to the surface is the force due to the spring, so the net force must be equal to the force of the spring:

Substituting the equations of motion for x and a gives us

Cancelling out like terms and solving for the angular frequency yields

The angular frequency depends only on the force constant and the mass, and not the amplitude. The angular frequency is defined as ω = 2 π / T , ω = 2 π / T , which yields an equation for the period of the motion:

The period also depends only on the mass and the force constant. The greater the mass, the longer the period. The stiffer the spring, the shorter the period. The frequency is

Vertical Motion and a Horizontal Spring

When a spring is hung vertically and a block is attached and set in motion, the block oscillates in SHM. In this case, there is no normal force, and the net effect of the force of gravity is to change the equilibrium position. Consider Figure 15.9 . Two forces act on the block: the weight and the force of the spring. The weight is constant and the force of the spring changes as the length of the spring changes.

When the block reaches the equilibrium position, as seen in Figure 15.9 , the force of the spring equals the weight of the block, F net = F s − m g = 0 F net = F s − m g = 0 , where

From the figure, the change in the position is Δ y = y 0 − y 1 Δ y = y 0 − y 1 and since − k ( − Δ y ) = m g − k ( − Δ y ) = m g , we have

If the block is displaced and released, it will oscillate around the new equilibrium position. As shown in Figure 15.10 , if the position of the block is recorded as a function of time, the recording is a periodic function.

If the block is displaced to a position y , the net force becomes F net = k ( y 0 − y ) − m g = 0 F net = k ( y 0 − y ) − m g = 0 . But we found that at the equilibrium position, m g = k Δ y = k y 0 − k y 1 m g = k Δ y = k y 0 − k y 1 . Substituting for the weight in the equation yields

Recall that y 1 y 1 is just the equilibrium position and any position can be set to be the point y = 0.00 m . y = 0.00 m . So let’s set y 1 y 1 to y = 0.00 m . y = 0.00 m . The net force then becomes

This is just what we found previously for a horizontally sliding mass on a spring. The constant force of gravity only served to shift the equilibrium location of the mass. Therefore, the solution should be the same form as for a block on a horizontal spring, y ( t ) = A cos ( ω t + ϕ ) . y ( t ) = A cos ( ω t + ϕ ) . The equations for the velocity and the acceleration also have the same form as for the horizontal case. Note that the inclusion of the phase shift means that the motion can actually be modeled using either a cosine or a sine function, since these two functions only differ by a phase shift.

As an Amazon Associate we earn from qualifying purchases.

This book may not be used in the training of large language models or otherwise be ingested into large language models or generative AI offerings without OpenStax's permission.

Want to cite, share, or modify this book? This book uses the Creative Commons Attribution License and you must attribute OpenStax.

Access for free at https://openstax.org/books/university-physics-volume-1/pages/1-introduction
  • Authors: William Moebs, Samuel J. Ling, Jeff Sanny
  • Publisher/website: OpenStax
  • Book title: University Physics Volume 1
  • Publication date: Sep 19, 2016
  • Location: Houston, Texas
  • Book URL: https://openstax.org/books/university-physics-volume-1/pages/1-introduction
  • Section URL: https://openstax.org/books/university-physics-volume-1/pages/15-1-simple-harmonic-motion

© Jan 19, 2024 OpenStax. Textbook content produced by OpenStax is licensed under a Creative Commons Attribution License . The OpenStax name, OpenStax logo, OpenStax book covers, OpenStax CNX name, and OpenStax CNX logo are not subject to the Creative Commons license and may not be reproduced without the prior and express written consent of Rice University.

Library homepage

  • school Campus Bookshelves
  • menu_book Bookshelves
  • perm_media Learning Objects
  • login Login
  • how_to_reg Request Instructor Account
  • hub Instructor Commons
  • Download Page (PDF)
  • Download Full Book (PDF)
  • Periodic Table
  • Physics Constants
  • Scientific Calculator
  • Reference & Cite
  • Tools expand_more
  • Readability

selected template will load here

This action is not available.

Physics LibreTexts

15.S: Oscillations (Summary)

  • Last updated
  • Save as PDF
  • Page ID 7699

Key Equations

15.1 simple harmonic motion.

  • Periodic motion is a repeating oscillation. The time for one oscillation is the period T and the number of oscillations per unit time is the frequency f. These quantities are related by \(f = \frac{1}{T}\).
  • Simple harmonic motion (SHM) is oscillatory motion for a system where the restoring force is proportional to the displacement and acts in the direction opposite to the displacement.
  • Maximum displacement is the amplitude A. The angular frequency \(\omega\), period T, and frequency f of a simple harmonic oscillator are given by \(\omega = \sqrt{\frac{k}{m}}\), T = 2\(\pi \sqrt{\frac{m}{k}}\), and f = \(\frac{1}{2 \pi} \sqrt{\frac{k}{m}}\), where m is the mass of the system and k is the force constant.
  • Displacement as a function of time in SHM is given by x(t) = Acos\(\left(\dfrac{2 \pi}{T} t + \phi \right)\) = Acos(\(\omega t + \phi\)).
  • The velocity is given by v(t) = -A\(\omega\)sin(\(\omega t + \phi\)) = -v max sin(\(\omega t + \phi\)), where v max = A\(\omega\) = A\(\sqrt{\frac{k}{m}}\).
  • The acceleration is given by a(t) = -A\(\omega^{2}\)cos(\(\omega t + \phi\)) = -a max cos(\(\omega t + \phi\)), where a max = A\(\omega^{2}\) = A\(\frac{k}{m}\).

15.2 Energy in Simple Harmonic Motion

  • The simplest type of oscillations are related to systems that can be described by Hooke’s law, F = −kx, where F is the restoring force, x is the displacement from equilibrium or deformation, and k is the force constant of the system.
  • Elastic potential energy U stored in the deformation of a system that can be described by Hooke’s law is given by U = \(\frac{1}{2}\)kx 2 .
  • Energy in the simple harmonic oscillator is shared between elastic potential energy and kinetic energy, with the total being constant: $$E_{Total} = \frac{1}{2} kx^{2} + \frac{1}{2} mv^{2} = \frac{1}{2} kA^{2} = constant \ldotp$$
  • The magnitude of the velocity as a function of position for the simple harmonic oscillator can be found by using $$v = \sqrt{\frac{k}{m} (A^{2} - x^{2})} \ldotp$$

15.3 Comparing Simple Harmonic Motion and Circular Motion

  • A projection of uniform circular motion undergoes simple harmonic oscillation.
  • Consider a circle with a radius A, moving at a constant angular speed \(\omega\). A point on the edge of the circle moves at a constant tangential speed of v max = A\(\omega\). The projection of the radius onto the x-axis is x(t) = Acos(\(\omega\)t + \(\phi\)), where (\(\phi\)) is the phase shift. The x-component of the tangential velocity is v(t) = −A\(\omega\)sin(\(\omega\)t + \(\phi\)).

15.4 Pendulums

  • A mass m suspended by a wire of length L and negligible mass is a simple pendulum and undergoes SHM for amplitudes less than about 15°. The period of a simple pendulum is T = 2\(\pi \sqrt{\frac{L}{g}}\), where L is the length of the string and g is the acceleration due to gravity.
  • The period of a physical pendulum T = 2\(\pi \sqrt{\frac{I}{mgL}}\) can be found if the moment of inertia is known. The length between the point of rotation and the center of mass is L.
  • The period of a torsional pendulum T = 2\(\pi \sqrt{\frac{I}{\kappa}}\) can be found if the moment of inertia and torsion constant are known.

15.5 Damped Oscillations

  • Damped harmonic oscillators have non-conservative forces that dissipate their energy.
  • Critical damping returns the system to equilibrium as fast as possible without overshooting.
  • An underdamped system will oscillate through the equilibrium position.
  • An overdamped system moves more slowly toward equilibrium than one that is critically damped.

15.6 Forced Oscillations

  • A system’s natural frequency is the frequency at which the system oscillates if not affected by driving or damping forces.
  • A periodic force driving a harmonic oscillator at its natural frequency produces resonance. The system is said to resonate.
  • The less damping a system has, the higher the amplitude of the forced oscillations near resonance. The more damping a system has, the broader response it has to varying driving frequencies.

Contributors and Attributions

Samuel J. Ling (Truman State University), Jeff Sanny (Loyola Marymount University), and Bill Moebs with many contributing authors. This work is licensed by OpenStax University Physics under a  Creative Commons Attribution License (by 4.0) .

Details & Upgrade Instructions

  • Purchases from within your account will upgrade your account immediately.
  • Purchases made from the homepage will be connected manually within 24 hours.
  • Please see below for PO and out-of-pocket teacher details.

Purchase Subscription (through July)

Log in   (independent user), create account, teacher registration, student registration, homeschooler / independent registration, teacher registration with google, teacher registration with google classroom, student registration with google.

Student account created! Click this button to use Google's login page to finish registration.

Reset Password

Physics equations & definitions, conversion factors, circular motion, gravitation, springs & oscillations, electro statics, electro magnetism, interactive practice problem:.

Fiveable

Find what you need to study

Practice Quizzes

Unit 6 Overview: Oscillations

5 min read • march 15, 2023

Riya Patel

Oscillations are seen everywhere, from the music we hear to the springs we play with, and even with some topics we'll cover in electricity and magnetism 👀. In Unit 6, we will delve into the world of oscillations and learn about various aspects such as simple harmonic motion , springs, pendulums, and wave motion.

The big idea of this unit surrounds the following question: How does the presence of restoring forces predict and lead to harmonic motion?

Key Vocabulary

  • Simple harmonic motion : A type of periodic motion in which the restoring force is proportional to the displacement from equilibrium position and acts in the opposite direction to the displacement.
  • Oscillation: The back-and-forth motion of an object about its equilibrium position.
  • Amplitude: The maximum displacement of an oscillating object from its equilibrium position.
  • Period : The time taken by an oscillating object to complete one cycle of motion.
  • Frequency : The number of cycles per unit time of an oscillating object.
  • Restoring force : The force that brings an oscillating object back to its equilibrium position.
  • Spring constant : The constant that relates the force exerted by a spring to its displacement from its equilibrium position.
  • Angular frequency : The rate at which an oscillating object completes one cycle of motion in radians per unit time.
  • Phase angle : The initial angle of an oscillating object at the start of its motion.
  • Resonance : A phenomenon in which an object is forced to vibrate at its natural frequency due to the application of an external force at the same frequency .

Some questions that can be explored in this unit are:

  • How does the period of oscillation of a mass-spring system vary with the mass of the object and the spring constant ?
  • How does the period of oscillation of a simple pendulum vary with the length of the string and the acceleration due to gravity?
  • How does the energy of a mass-spring system vary during oscillation?
  • How does the amplitude of a mass-spring system vary with the initial displacement?
  • What is resonance and how does it occur in mass-spring systems and simple pendulums?

6.1 Simple Harmonic Motion , Springs, and Pendulums

Simple harmonic motion (SHM) is a type of periodic motion in which the restoring force is proportional to the displacement from equilibrium position and acts in the opposite direction to the displacement. This results in a sinusoidal motion that is characterized by a constant period and amplitude. The equation for SHM is given by x(t) = A cos(ωt + φ), where A is the amplitude, ω is the angular frequency , and φ is the phase angle .

One of the most common examples of SHM is the motion of a mass attached to a spring. When the spring is stretched or compressed from its equilibrium position, it exerts a restoring force on the mass, which causes it to oscillate back and forth. The period of oscillation of the mass-spring system depends on the mass of the object and the spring constant .

Another example of SHM is the motion of a simple pendulum . A simple pendulum consists of a mass attached to a weightless, flexible string or rod that is suspended from a fixed point. When the mass is displaced from its equilibrium position, it experiences a restoring force due to gravity, which causes it to oscillate back and forth. The period of oscillation of the pendulum depends on the length of the string and the acceleration due to gravity.

Practice Problems

Here are some practice problems related to simple harmonic motion , springs, and pendulums:.

A mass of 0.2 kg is attached to a spring with a spring constant of 20 N/m. What is the period of oscillation of the mass-spring system ?

A pendulum of length 1 m is displaced from its equilibrium position by an angle of 10 degrees. What is the period of oscillation of the pendulum?

A mass-spring system has an amplitude of 5 cm and a period of 0.4 s. What is the maximum velocity of the mass during oscillation?

A pendulum has a period of 2 s on Earth. What would be its period on the moon, where the acceleration due to gravity is one-sixth of that on Earth?

A mass of 0.5 kg is attached to a spring with a spring constant of 10 N/m. If the mass is initially displaced by 0.2 m from its equilibrium position, what is its maximum potential energy during oscillation?

The period of oscillation of a mass-spring system is given by T = 2π√(m/k), where m is the mass of the object and k is the spring constant . Plugging in the values, we get T = 2π√(0.2/20) = 0.628 s.

The period of oscillation of a simple pendulum is given by T = 2π√(l/g), where l is the length of the string and g is the acceleration due to gravity. Plugging in the values, we get T = 2π√(1/9.81) = 2.006 s.

The maximum velocity of a mass-spring system is given by vmax = Aω, where A is the amplitude and ω is the angular frequency (ω = 2π/T). Plugging in the values, we get vmax = (0.05 m) × (2π/0.4 s) = 0.785 m/s.

The period of oscillation of a simple pendulum is independent of the mass of the pendulum and is only dependent on the length of the string and the acceleration due to gravity. Therefore, the period of the pendulum on the moon would also be 2 s.

The maximum potential energy of a mass-spring system is given by Umax = 1/2kA^2, where k is the spring constant and A is the amplitude. Plugging in the values, we get Umax = (1/2) × 10 × (0.2)^2 = 0.2 J.

Fiveable

Student Wellness

Stay connected.

© 2024 Fiveable Inc. All rights reserved.

Learn AP Physics

Ap physics c - oscillatory motion.

Many systems in nature exhibit motion that periodically repeats itself. A special type of periodic motion is Simple Harmonic motion, which can be used to describe the motion of pendulums and mass-spring systems.

Oscillatory Motion Video Lessons

Multiple-choice practice problems.

Scroll down to see multiple choice practice problems in oscillation.

solution

Chapter: 11th Physics : UNIT 10 : Oscillations

Solved example problems for physics: oscillations, numerical problems.

1. Consider the Earth as a homogeneous sphere of radius R and a straight hole is bored in it through its centre. Show that a particle dropped into the hole will execute a simple harmonic motion such that its time period is

physics practice problems oscillation

Earth is assumed to be a homogeneous sphere.

Its centre is at O and Radius = R

The hole is bored straight through the centre along its diameter. The acceleration due to gravity at the surface of the earth =  g

Mass of the body dropped inside the hole =  m

After time t, the depth it reached (inside the earth) =  d

The value of ‘g’ decreases with deportation.

So acceleration due to gravity at deportation = ‘ g '

i.e.,g' = g(l - d //R) = g( (R- d ) / R) ...(1)

Let  y  be the distance from the centre of the earth

Then y = Radius - distance = R - d

Substitute y in (1)

g' = g  y /R

Now, force on the body of mass m due to this new acceleration g' will be

F = mg' = mg y  /R

and this force is directed towards the mean position O.

The body dropped in the hole will execute S.H.M Spring factor k =  mg /Radius

physics practice problems oscillation

2. Calculate the time period of the oscillation of a particle of mass m moving in the potential defined as

physics practice problems oscillation

where E is the total energy of the particle.

Length of simple pendulum  l  = 0.9 m

Inclined plane with the horizontal plane α = 45°

Time period of oscillation of simple pendulum T = ?

physics practice problems oscillation

3. Consider a simple pendulum of length  l  = 0.9  m  which is properly placed on a   trolley rolling down on a inclined plane which is at  θ  = 45° with the horizontal. Assuming that the inclined plane is frictionless, calculate the time period of oscillation of the simple pendulum.

Answer:  0.86 s

physics practice problems oscillation

Spring factor of liquid = Aρg

Inertra factor of wood piece =  m

physics practice problems oscillation

5. Consider two simple harmonic motion along  x  and  y -axis having same frequencies but different amplitudes as  x  = A sin (ω t  + φ) (along  x  axis) and  y =  B sin ω t  (along  y  axis). Then show that

physics practice problems oscillation

and also discuss the special cases when

physics practice problems oscillation

Note:  when a particle is subjected to two   simple harmonic motion at right angle to each other the particle may move along different paths. Such paths are called Lissajous figures.

a. y=B/A x equation  is  a  straight  line passing through origin with positive slope.

b.   y= - B/A x  equation is a straight line passing through origin with negative slope.

physics practice problems oscillation

d.  x 2 + y 2   =  A 2 , equation is a circle whose center is origin .

physics practice problems oscillation

6. Show that for a particle executing simple harmonic motion

a. the average value of kinetic energy is equal to the average value of potential energy.

b. average potential energy = average  kinetic energy = ½ (total energy)

Hint :  average kinetic energy  = < kinetic energy > = 1/T ∫ 0 T ( Kinetic energy )   and average Potential energy = <Potential energy> =1/T ∫ 0 T ( Potential energy )

physics practice problems oscillation

7. Compute the time period for the following system if the block of mass m is slightly displaced vertically down from its equilibrium position and then released. Assume that the pulley is light and smooth, strings and springs are light.

physics practice problems oscillation

Hint and answer:

Pulley is fixed rigidly here. When the mass displace by  y  and the spring will also stretch by  y . Therefore,  F  =  T  =  ky

physics practice problems oscillation

Mass displace by  y , pulley also displaces by  y. T  = 4 ky .

physics practice problems oscillation

Displacement, velocity, acceleration and its graphical representation – SHM

Example 10.3.

Which of the following represent simple harmonic motion?

(i)  x  =  A  sin ω t  + B cos  ωt

(ii)  x  =  A  sin ωt+ B cos 2 ωt

(iii)  x  =  A e iωt

(iv)  x  =  A  ln  ωt

(i)  x  =  A  sin ω t  +  B  cos  ωt

physics practice problems oscillation

This differential equation is similar to the differential equation of SHM (equation 10.10).

Therefore,  x  =  A  sin  ωt + B  cos  ωt  represents SHM.

(ii)  x  =A sin  ωt  +  B  cos2 ωt

physics practice problems oscillation

This differential equation is not like the differential equation of a SHM (equation 10.10). Therefore,  x  =  A  sin  ωt  +  B  cos 2 ωt  does not represent SHM.

 (iii) x=Ae j ω t

physics practice problems oscillation

This differential equation is like the differential equation of SHM (equation 10.10). Therefore,  x  =  A e iωt represents SHM.

(iv)  x  =  A ln  ω t

physics practice problems oscillation

This differential equation is not like the differential equation of a SHM (equation 10.10). Therefore,  x  =  A  ln ω t  does not represent SHM.

EXAMPLE 10.4

Consider a particle undergoing simple harmonic motion. The velocity of the particle at position  x 1  is  v 1  and velocity of the particle at position  x 2  is  v 2 . Show that the ratio of time period and amplitude is

physics practice problems oscillation

EXAMPLE 10.5

A nurse measured the average heart beats of a patient and reported to the doctor in terms of time period as 0.8 s . Express the heart beat of the patient in terms of number of beats measured per minute.

Let the number of heart beats measured be  f . Since the time period is inversely proportional to the heart beat, then

physics practice problems oscillation

EXAMPLE 10.6

Calculate the amplitude, angular frequency, frequency, time period and initial phase for the simple harmonic oscillation given below

a. y  = 0.3 sin (40πt + 1.1)

b.  y  = 2 cos (πt)

c.  y  = 3 sin (2πt − 1.5)

Simple harmonic oscillation equation is y = A sin(ωt + φ 0 ) or y =A cos(ωt + φ 0 )

physics practice problems oscillation

EXAMPLE 10.7

Show that for a simple harmonic motion, the phase difference between

a. displacement and velocity is π/2 radian or 90°.

b. velocity and acceleration is π/2 radian or 90°.

c.  displacement and acceleration is π radian or 180°.

a.    The displacement of the particle executing simple harmonic motion

y  =  A  sinω t

Velocity of the particle is

v  = Aωcos ωt = Aωsin(ωt+ π /2)

The phase difference between displacement and velocity is π/2.

b. The velocity of the particle is

v = A ω cos ωt

Acceleration of the particle is

a  = Aω 2 sin ω t = Aω 2 cos(ωt+ π /2)

The phase difference between velocity and acceleration is π/2.

c. The displacement of the particle is  y  =  A  sinω t

a  = −  A  ω 2   sin ω t  = A ω 2   sin(ω t  + π)

The phase difference between displacement and acceleration is π.

Solved Example Problems for Linear Simple Harmonic Oscillator (LHO)

Vertical oscillations of a spring, example 10.8.

A spring balance has a scale which ranges from 0 to 25 kg and the length of the scale is 0.25m. It is taken to an unknown planet X where the acceleration due to gravity is 11.5 m s −1 . Suppose a body of mass M kg is suspended in this spring and made to oscillate with a period of 0.50 s. Compute the gravitational force acting on the body.

Let us first calculate the stiffness constant of the spring balance by using equation (10.29),

physics practice problems oscillation

The time period of oscillations is given by T=2π√M/√ k , , where M is the mass of the body.

Since, M is unknown, rearranging, we get

physics practice problems oscillation

The gravitational force acting on the body is W = Mg = 7.3 × 11.5 = 83.95 N ≈ 84 N

Combinations of springs

Example 10.9.

Consider two springs whose force constants are 1 N m −1  and 2 N m −1  which are connected in series. Calculate the effective spring constant ( k s  ) and comment on  k s  .

physics practice problems oscillation

k s   <  k 1   and  k s   <  k

Therefore, the effective spring constant is lesser than both  k 1  and  k 2 .

EXAMPLE 10.10

Consider two springs with force constants 1 N m −1  and 2 N m −1  connected in parallel. Calculate the effective spring constant ( k p  ) and comment on  k p .

k 1   = 1 N m −1 ,  k 2   = 2 N m −1

k p   =  k 1   +  k 2   N m −1

k p   = 1 + 2 = 3 N m −1

k p   >  k 1   and  k p   >  k 2

Therefore, the effective spring constant is greater than both  k 1  and  k 2 .

EXAMPLE 10.11

Calculate the equivalent spring constant for the following systems and also compute if all the spring constants are equal:

physics practice problems oscillation

a. Since  k 1  and  k 2  are parallel,  k u  =  k 1  +  k 2  Similarly,  k 3  and  k 4  are parallel, therefore,  k d  =  k 3  +  k 4

But  k u  and  k d  are in series,

physics practice problems oscillation

If all the spring constants are equal then,  k 1  =  k 2  =  k 3  =  k 4  =  k

Which means,  k u  = 2 k  and  k d  = 2 k

physics practice problems oscillation

b. Since  k 1  and  k 2  are parallel,  k A  =  k 1  +  k 2  Similarly,  k 4  and  k 5  are parallel, therefore,  k B  =  k 4  +  k 5

But  k A ,  k 3 ,  k B , and  k 6  are in series,

physics practice problems oscillation

If all the spring constants are equal then,  k 1  =  k 2  =  k 3  =  k 4  =  k 5  =  k 6  =  k  which means,  k A  = 2 k  and  k B  = 2 k

physics practice problems oscillation

k eq   = k/3

EXAMPLE 10.12

A mass  m  moves with a speed  v  on a horizontal smooth surface and collides with a nearly massless spring whose spring constant is  k . If the mass stops after collision, compute the maximum compression of the spring.

When the mass collides with the spring, from the law of conservation of energy “the loss in kinetic energy of mass is gain in elastic potential energy by spring”.

Let  x  be the distance of compression of spring, then the law of conservation of energy

physics practice problems oscillation

Oscillations of a simple pendulum in SHM and laws of simple pendulum

Example 10.13.

In simple pendulum experiment, we have used small angle approximation . Discuss the small angle approximation.

physics practice problems oscillation

For θ in radian, sin θ ≈ θ for very small angles

physics practice problems oscillation

This means that “for  θ  as large as 10 degrees, sin  θ  is nearly the same as  θ  when  θ   is expressed in radians”. As  θ  increases in value sin θ  gradually becomes different from  θ

EXAMPLE 10.14

If the length of the simple pendulum is increased by 44% from its original length, calculate the percentage increase in time period of the pendulum.

physics practice problems oscillation

Solved Example Problems for Energy in Simple Harmonic Motion

Example 10.15.

Write down the kinetic energy and total energy expressions in terms of linear momentum, For one-dimensional case.

Kinetic energy is  KE =   1/2  mv x 2

Multiply numerator and denominator by  m

KE =   [ 1/2 m ]  m 2  v x 2   = [ 1/2 m]   (m v x   ) 2   =   [ 1/2 m ]  p x 2

where,  p x  is the linear momentum of the particle executing simple harmonic motion.

Total energy can be written as sum of kinetic energy and potential energy, therefore, from equation (10.73) and also from equation (10.75), we get

E =  KE  + U (  x )   =   [ 1/2 m ]  p x 2   +   1/2  m ω 2  x 2   =   constant

physics practice problems oscillation

EXAMPLE 10.16

Compute the position of an oscillating particle when its kinetic energy and potential energy are equal.

Since the kinetic energy and potential energy of the oscillating particle are equal,

1/2  m ω   2   (A 2   −  x  2   )   =   1/2  m ω 2  x 2

A 2   −  x 2   =  x 2

Related Topics

Privacy Policy , Terms and Conditions , DMCA Policy and Compliant

Copyright © 2018-2024 BrainKart.com; All Rights Reserved. Developed by Therithal info, Chennai.

Browse Course Material

Course info.

  • Prof. Yen-Jie Lee

Departments

As taught in.

  • Atomic, Molecular, Optical Physics
  • Classical Mechanics
  • Electromagnetism

Learning Resource Types

Physics iii: vibrations and waves.

« Previous | Next »

Exam Information

Practice exams.

Final Exam Formula Sheet (PDF)  

Practice Final Exam 1 (PDF)

Practice Final Exam 2 (PDF - 1.3MB)

Practice Final Exam 3 (PDF)    

MIT Open Learning

Youtube

  • TPC and eLearning
  • Read Watch Interact
  • What's NEW at TPC?
  • Practice Review Test
  • Teacher-Tools
  • Subscription Selection
  • Seat Calculator
  • Ad Free Account
  • Edit Profile Settings
  • Classes (Version 2)
  • Student Progress Edit
  • Task Properties
  • Export Student Progress
  • Task, Activities, and Scores
  • Metric Conversions Questions
  • Metric System Questions
  • Metric Estimation Questions
  • Significant Digits Questions
  • Proportional Reasoning
  • Acceleration
  • Distance-Displacement
  • Dots and Graphs
  • Graph That Motion
  • Match That Graph
  • Name That Motion
  • Motion Diagrams
  • Pos'n Time Graphs Numerical
  • Pos'n Time Graphs Conceptual
  • Up And Down - Questions
  • Balanced vs. Unbalanced Forces
  • Change of State
  • Force and Motion
  • Mass and Weight
  • Match That Free-Body Diagram
  • Net Force (and Acceleration) Ranking Tasks
  • Newton's Second Law
  • Normal Force Card Sort
  • Recognizing Forces
  • Air Resistance and Skydiving
  • Solve It! with Newton's Second Law
  • Which One Doesn't Belong?
  • Component Addition Questions
  • Head-to-Tail Vector Addition
  • Projectile Mathematics
  • Trajectory - Angle Launched Projectiles
  • Trajectory - Horizontally Launched Projectiles
  • Vector Addition
  • Vector Direction
  • Which One Doesn't Belong? Projectile Motion
  • Forces in 2-Dimensions
  • Being Impulsive About Momentum
  • Explosions - Law Breakers
  • Hit and Stick Collisions - Law Breakers
  • Case Studies: Impulse and Force
  • Impulse-Momentum Change Table
  • Keeping Track of Momentum - Hit and Stick
  • Keeping Track of Momentum - Hit and Bounce
  • What's Up (and Down) with KE and PE?
  • Energy Conservation Questions
  • Energy Dissipation Questions
  • Energy Ranking Tasks
  • LOL Charts (a.k.a., Energy Bar Charts)
  • Match That Bar Chart
  • Words and Charts Questions
  • Name That Energy
  • Stepping Up with PE and KE Questions
  • Case Studies - Circular Motion
  • Circular Logic
  • Forces and Free-Body Diagrams in Circular Motion
  • Gravitational Field Strength
  • Universal Gravitation
  • Angular Position and Displacement
  • Linear and Angular Velocity
  • Angular Acceleration
  • Rotational Inertia
  • Balanced vs. Unbalanced Torques
  • Getting a Handle on Torque
  • Torque-ing About Rotation
  • Properties of Matter
  • Fluid Pressure
  • Buoyant Force
  • Sinking, Floating, and Hanging
  • Pascal's Principle
  • Flow Velocity
  • Bernoulli's Principle
  • Balloon Interactions
  • Charge and Charging
  • Charge Interactions
  • Charging by Induction
  • Conductors and Insulators
  • Coulombs Law
  • Electric Field
  • Electric Field Intensity
  • Polarization
  • Case Studies: Electric Power
  • Know Your Potential
  • Light Bulb Anatomy
  • I = ∆V/R Equations as a Guide to Thinking
  • Parallel Circuits - ∆V = I•R Calculations
  • Resistance Ranking Tasks
  • Series Circuits - ∆V = I•R Calculations
  • Series vs. Parallel Circuits
  • Equivalent Resistance
  • Period and Frequency of a Pendulum
  • Pendulum Motion: Velocity and Force
  • Energy of a Pendulum
  • Period and Frequency of a Mass on a Spring
  • Horizontal Springs: Velocity and Force
  • Vertical Springs: Velocity and Force
  • Energy of a Mass on a Spring
  • Decibel Scale
  • Frequency and Period
  • Closed-End Air Columns
  • Name That Harmonic: Strings
  • Rocking the Boat
  • Wave Basics
  • Matching Pairs: Wave Characteristics
  • Wave Interference
  • Waves - Case Studies
  • Color Addition and Subtraction
  • Color Filters
  • If This, Then That: Color Subtraction
  • Light Intensity
  • Color Pigments
  • Converging Lenses
  • Curved Mirror Images
  • Law of Reflection
  • Refraction and Lenses
  • Total Internal Reflection
  • Who Can See Who?
  • Formulas and Atom Counting
  • Atomic Models
  • Bond Polarity
  • Entropy Questions
  • Cell Voltage Questions
  • Heat of Formation Questions
  • Reduction Potential Questions
  • Oxidation States Questions
  • Measuring the Quantity of Heat
  • Hess's Law
  • Oxidation-Reduction Questions
  • Galvanic Cells Questions
  • Thermal Stoichiometry
  • Molecular Polarity
  • Quantum Mechanics
  • Balancing Chemical Equations
  • Bronsted-Lowry Model of Acids and Bases
  • Classification of Matter
  • Collision Model of Reaction Rates
  • Density Ranking Tasks
  • Dissociation Reactions
  • Complete Electron Configurations
  • Enthalpy Change Questions
  • Equilibrium Concept
  • Equilibrium Constant Expression
  • Equilibrium Calculations - Questions
  • Equilibrium ICE Table
  • Ionic Bonding
  • Lewis Electron Dot Structures
  • Line Spectra Questions
  • Measurement and Numbers
  • Metals, Nonmetals, and Metalloids
  • Metric Estimations
  • Metric System
  • Molarity Ranking Tasks
  • Mole Conversions
  • Name That Element
  • Names to Formulas
  • Names to Formulas 2
  • Nuclear Decay
  • Particles, Words, and Formulas
  • Periodic Trends
  • Precipitation Reactions and Net Ionic Equations
  • Pressure Concepts
  • Pressure-Temperature Gas Law
  • Pressure-Volume Gas Law
  • Chemical Reaction Types
  • Significant Digits and Measurement
  • States Of Matter Exercise
  • Stoichiometry - Math Relationships
  • Subatomic Particles
  • Spontaneity and Driving Forces
  • Gibbs Free Energy
  • Volume-Temperature Gas Law
  • Acid-Base Properties
  • Energy and Chemical Reactions
  • Chemical and Physical Properties
  • Valence Shell Electron Pair Repulsion Theory
  • Writing Balanced Chemical Equations
  • Mission CG1
  • Mission CG10
  • Mission CG2
  • Mission CG3
  • Mission CG4
  • Mission CG5
  • Mission CG6
  • Mission CG7
  • Mission CG8
  • Mission CG9
  • Mission EC1
  • Mission EC10
  • Mission EC11
  • Mission EC12
  • Mission EC2
  • Mission EC3
  • Mission EC4
  • Mission EC5
  • Mission EC6
  • Mission EC7
  • Mission EC8
  • Mission EC9
  • Mission RL1
  • Mission RL2
  • Mission RL3
  • Mission RL4
  • Mission RL5
  • Mission RL6
  • Mission KG7
  • Mission RL8
  • Mission KG9
  • Mission RL10
  • Mission RL11
  • Mission RM1
  • Mission RM2
  • Mission RM3
  • Mission RM4
  • Mission RM5
  • Mission RM6
  • Mission RM8
  • Mission RM10
  • Mission LC1
  • Mission RM11
  • Mission LC2
  • Mission LC3
  • Mission LC4
  • Mission LC5
  • Mission LC6
  • Mission LC8
  • Mission SM1
  • Mission SM2
  • Mission SM3
  • Mission SM4
  • Mission SM5
  • Mission SM6
  • Mission SM8
  • Mission SM10
  • Mission KG10
  • Mission SM11
  • Mission KG2
  • Mission KG3
  • Mission KG4
  • Mission KG5
  • Mission KG6
  • Mission KG8
  • Mission KG11
  • Mission F2D1
  • Mission F2D2
  • Mission F2D3
  • Mission F2D4
  • Mission F2D5
  • Mission F2D6
  • Mission KC1
  • Mission KC2
  • Mission KC3
  • Mission KC4
  • Mission KC5
  • Mission KC6
  • Mission KC7
  • Mission KC8
  • Mission AAA
  • Mission SM9
  • Mission LC7
  • Mission LC9
  • Mission NL1
  • Mission NL2
  • Mission NL3
  • Mission NL4
  • Mission NL5
  • Mission NL6
  • Mission NL7
  • Mission NL8
  • Mission NL9
  • Mission NL10
  • Mission NL11
  • Mission NL12
  • Mission MC1
  • Mission MC10
  • Mission MC2
  • Mission MC3
  • Mission MC4
  • Mission MC5
  • Mission MC6
  • Mission MC7
  • Mission MC8
  • Mission MC9
  • Mission RM7
  • Mission RM9
  • Mission RL7
  • Mission RL9
  • Mission SM7
  • Mission SE1
  • Mission SE10
  • Mission SE11
  • Mission SE12
  • Mission SE2
  • Mission SE3
  • Mission SE4
  • Mission SE5
  • Mission SE6
  • Mission SE7
  • Mission SE8
  • Mission SE9
  • Mission VP1
  • Mission VP10
  • Mission VP2
  • Mission VP3
  • Mission VP4
  • Mission VP5
  • Mission VP6
  • Mission VP7
  • Mission VP8
  • Mission VP9
  • Mission WM1
  • Mission WM2
  • Mission WM3
  • Mission WM4
  • Mission WM5
  • Mission WM6
  • Mission WM7
  • Mission WM8
  • Mission WE1
  • Mission WE10
  • Mission WE2
  • Mission WE3
  • Mission WE4
  • Mission WE5
  • Mission WE6
  • Mission WE7
  • Mission WE8
  • Mission WE9
  • Vector Walk Interactive
  • Name That Motion Interactive
  • Kinematic Graphing 1 Concept Checker
  • Kinematic Graphing 2 Concept Checker
  • Graph That Motion Interactive
  • Rocket Sled Concept Checker
  • Force Concept Checker
  • Free-Body Diagrams Concept Checker
  • Free-Body Diagrams The Sequel Concept Checker
  • Skydiving Concept Checker
  • Elevator Ride Concept Checker
  • Vector Addition Concept Checker
  • Vector Walk in Two Dimensions Interactive
  • Name That Vector Interactive
  • River Boat Simulator Concept Checker
  • Projectile Simulator 2 Concept Checker
  • Projectile Simulator 3 Concept Checker
  • Turd the Target 1 Interactive
  • Turd the Target 2 Interactive
  • Balance It Interactive
  • Go For The Gold Interactive
  • Egg Drop Concept Checker
  • Fish Catch Concept Checker
  • Exploding Carts Concept Checker
  • Collision Carts - Inelastic Collisions Concept Checker
  • Its All Uphill Concept Checker
  • Stopping Distance Concept Checker
  • Chart That Motion Interactive
  • Roller Coaster Model Concept Checker
  • Uniform Circular Motion Concept Checker
  • Horizontal Circle Simulation Concept Checker
  • Vertical Circle Simulation Concept Checker
  • Race Track Concept Checker
  • Gravitational Fields Concept Checker
  • Orbital Motion Concept Checker
  • Balance Beam Concept Checker
  • Torque Balancer Concept Checker
  • Aluminum Can Polarization Concept Checker
  • Charging Concept Checker
  • Name That Charge Simulation
  • Coulomb's Law Concept Checker
  • Electric Field Lines Concept Checker
  • Put the Charge in the Goal Concept Checker
  • Circuit Builder Concept Checker (Series Circuits)
  • Circuit Builder Concept Checker (Parallel Circuits)
  • Circuit Builder Concept Checker (∆V-I-R)
  • Circuit Builder Concept Checker (Voltage Drop)
  • Equivalent Resistance Interactive
  • Pendulum Motion Simulation Concept Checker
  • Mass on a Spring Simulation Concept Checker
  • Particle Wave Simulation Concept Checker
  • Boundary Behavior Simulation Concept Checker
  • Slinky Wave Simulator Concept Checker
  • Simple Wave Simulator Concept Checker
  • Wave Addition Simulation Concept Checker
  • Standing Wave Maker Simulation Concept Checker
  • Color Addition Concept Checker
  • Painting With CMY Concept Checker
  • Stage Lighting Concept Checker
  • Filtering Away Concept Checker
  • InterferencePatterns Concept Checker
  • Young's Experiment Interactive
  • Plane Mirror Images Interactive
  • Who Can See Who Concept Checker
  • Optics Bench (Mirrors) Concept Checker
  • Name That Image (Mirrors) Interactive
  • Refraction Concept Checker
  • Total Internal Reflection Concept Checker
  • Optics Bench (Lenses) Concept Checker
  • Kinematics Preview
  • Velocity Time Graphs Preview
  • Moving Cart on an Inclined Plane Preview
  • Stopping Distance Preview
  • Cart, Bricks, and Bands Preview
  • Fan Cart Study Preview
  • Friction Preview
  • Coffee Filter Lab Preview
  • Friction, Speed, and Stopping Distance Preview
  • Up and Down Preview
  • Projectile Range Preview
  • Ballistics Preview
  • Juggling Preview
  • Marshmallow Launcher Preview
  • Air Bag Safety Preview
  • Colliding Carts Preview
  • Collisions Preview
  • Engineering Safer Helmets Preview
  • Push the Plow Preview
  • Its All Uphill Preview
  • Energy on an Incline Preview
  • Modeling Roller Coasters Preview
  • Hot Wheels Stopping Distance Preview
  • Ball Bat Collision Preview
  • Energy in Fields Preview
  • Weightlessness Training Preview
  • Roller Coaster Loops Preview
  • Universal Gravitation Preview
  • Keplers Laws Preview
  • Kepler's Third Law Preview
  • Charge Interactions Preview
  • Sticky Tape Experiments Preview
  • Wire Gauge Preview
  • Voltage, Current, and Resistance Preview
  • Light Bulb Resistance Preview
  • Series and Parallel Circuits Preview
  • Thermal Equilibrium Preview
  • Linear Expansion Preview
  • Heating Curves Preview
  • Electricity and Magnetism - Part 1 Preview
  • Electricity and Magnetism - Part 2 Preview
  • Vibrating Mass on a Spring Preview
  • Period of a Pendulum Preview
  • Wave Speed Preview
  • Slinky-Experiments Preview
  • Standing Waves in a Rope Preview
  • Sound as a Pressure Wave Preview
  • DeciBel Scale Preview
  • DeciBels, Phons, and Sones Preview
  • Sound of Music Preview
  • Shedding Light on Light Bulbs Preview
  • Models of Light Preview
  • Electromagnetic Radiation Preview
  • Electromagnetic Spectrum Preview
  • EM Wave Communication Preview
  • Digitized Data Preview
  • Light Intensity Preview
  • Concave Mirrors Preview
  • Object Image Relations Preview
  • Snells Law Preview
  • Reflection vs. Transmission Preview
  • Magnification Lab Preview
  • Reactivity Preview
  • Ions and the Periodic Table Preview
  • Periodic Trends Preview
  • Gaining Teacher Access
  • Tasks and Classes
  • Tasks - Classic
  • Subscription
  • Subscription Locator
  • 1-D Kinematics
  • Newton's Laws
  • Vectors - Motion and Forces in Two Dimensions
  • Momentum and Its Conservation
  • Work and Energy
  • Circular Motion and Satellite Motion
  • Thermal Physics
  • Static Electricity
  • Electric Circuits
  • Vibrations and Waves
  • Sound Waves and Music
  • Light and Color
  • Reflection and Mirrors
  • About the Physics Interactives
  • Task Tracker
  • Usage Policy
  • Newtons Laws
  • Vectors and Projectiles
  • Forces in 2D
  • Momentum and Collisions
  • Circular and Satellite Motion
  • Balance and Rotation
  • Electromagnetism
  • Waves and Sound
  • Forces in Two Dimensions
  • Work, Energy, and Power
  • Circular Motion and Gravitation
  • Sound Waves
  • 1-Dimensional Kinematics
  • Circular, Satellite, and Rotational Motion
  • Einstein's Theory of Special Relativity
  • Waves, Sound and Light
  • QuickTime Movies
  • About the Concept Builders
  • Pricing For Schools
  • Directions for Version 2
  • Measurement and Units
  • Relationships and Graphs
  • Rotation and Balance
  • Vibrational Motion
  • Reflection and Refraction
  • Teacher Accounts
  • Task Tracker Directions
  • Kinematic Concepts
  • Kinematic Graphing
  • Wave Motion
  • Sound and Music
  • About CalcPad
  • 1D Kinematics
  • Vectors and Forces in 2D
  • Simple Harmonic Motion
  • Rotational Kinematics
  • Rotation and Torque
  • Rotational Dynamics
  • Electric Fields, Potential, and Capacitance
  • Transient RC Circuits
  • Light Waves
  • Units and Measurement
  • Stoichiometry
  • Molarity and Solutions
  • Thermal Chemistry
  • Acids and Bases
  • Kinetics and Equilibrium
  • Solution Equilibria
  • Oxidation-Reduction
  • Nuclear Chemistry
  • NGSS Alignments
  • 1D-Kinematics
  • Projectiles
  • Circular Motion
  • Magnetism and Electromagnetism
  • Graphing Practice
  • About the ACT
  • ACT Preparation
  • For Teachers
  • Other Resources
  • Newton's Laws of Motion
  • Work and Energy Packet
  • Static Electricity Review
  • Solutions Guide
  • Solutions Guide Digital Download
  • Motion in One Dimension
  • Work, Energy and Power
  • Frequently Asked Questions
  • Purchasing the Download
  • Purchasing the CD
  • Purchasing the Digital Download
  • About the NGSS Corner
  • NGSS Search
  • Force and Motion DCIs - High School
  • Energy DCIs - High School
  • Wave Applications DCIs - High School
  • Force and Motion PEs - High School
  • Energy PEs - High School
  • Wave Applications PEs - High School
  • Crosscutting Concepts
  • The Practices
  • Physics Topics
  • NGSS Corner: Activity List
  • NGSS Corner: Infographics
  • About the Toolkits
  • Position-Velocity-Acceleration
  • Position-Time Graphs
  • Velocity-Time Graphs
  • Newton's First Law
  • Newton's Second Law
  • Newton's Third Law
  • Terminal Velocity
  • Projectile Motion
  • Forces in 2 Dimensions
  • Impulse and Momentum Change
  • Momentum Conservation
  • Work-Energy Fundamentals
  • Work-Energy Relationship
  • Roller Coaster Physics
  • Satellite Motion
  • Electric Fields
  • Circuit Concepts
  • Series Circuits
  • Parallel Circuits
  • Describing-Waves
  • Wave Behavior Toolkit
  • Standing Wave Patterns
  • Resonating Air Columns
  • Wave Model of Light
  • Plane Mirrors
  • Curved Mirrors
  • Teacher Guide
  • Using Lab Notebooks
  • Current Electricity
  • Light Waves and Color
  • Reflection and Ray Model of Light
  • Refraction and Ray Model of Light
  • Classes (Legacy Version)
  • Teacher Resources
  • Subscriptions

physics practice problems oscillation

  • Newton's Laws
  • Einstein's Theory of Special Relativity
  • About Concept Checkers
  • School Pricing
  • Newton's Laws of Motion
  • Newton's First Law
  • Newton's Third Law

Mechanics: Simple Harmonic Motion

IMAGES

  1. Learn AP Physics

    physics practice problems oscillation

  2. Oscillations Problems with Solution One

    physics practice problems oscillation

  3. Unit 5 Physics Oscillations Questions

    physics practice problems oscillation

  4. Learn AP Physics

    physics practice problems oscillation

  5. Learn AP Physics

    physics practice problems oscillation

  6. NCERT Solutions for Class 11 Physics Chapter 14 Oscillations

    physics practice problems oscillation

VIDEO

  1. SHM L02

  2. Physics Lab 4-Oscillations

  3. Oscillations

  4. A PARTICLE EXECUTES SHM SUCH THATTHE MAX VELOCITY DURING OSCILLATION EQUAL TO MAX ACCELERATION # TS

  5. Oscillations part 1, periodic & oscillatory motion,SHM, Equation for displacement and velocity

  6. WHAT IS OSCILLATION ?

COMMENTS

  1. 16: Oscillatory Motion and Waves (Exercises)

    Solution. (a) Period increases by a factor of 1.41 ( 2-√ 2) (b) Period decreases to 97.5% of old period. 49. Find the ratio of the new/old periods of a pendulum if the pendulum were transported from Earth to the Moon, where the acceleration due to gravity is 1.63m/s2 1.63 m / s 2.

  2. Oscillations and Simple Harmonic Motion: Problems 1

    Problems 1 Previous Next Problem : An object in circular motion has an easily defined period, frequency and angular velocity. Can circular motion be considered an oscillation? Though circular motion has many similarities to oscillations, it can not truly be considered an oscillation.

  3. AP Physics 1: Oscillations Multiple-Choice Practice Questions

    1. A block attached to an ideal spring undergoes simple harmonic motion. The acceleration of the block has its maximum magnitude at the point where. A. the speed is the maximum. B. the speed is the minimum. C. the restoring force is the minimum. D. the kinetic energy is the maximum. 2.

  4. Simple Harmonic Oscillator

    acceleration elastic potential energy kinetic energy net force speed Given an object oscillating horizontally in simple harmonic motion, which graph of energy vs. displacement shown below… best represents… the total energy of the object-spring system? the kinetic energy of the object? the potential energy of the spring? Explain your reasoning.

  5. 15.1 Simple Harmonic Motion

    For periodic motion, frequency is the number of oscillations per unit time. The relationship between frequency and period is. f = 1 T. f = 1 T. 15.1. The SI unit for frequency is the hertz (Hz) and is defined as one cycle per second: 1Hz = 1cycle s or 1Hz = 1 s = 1s−1. 1 Hz = 1 cycle s or 1 Hz = 1 s = 1 s −1.

  6. Vibrations and Waves Problem Sets

    Problem 25: A standing wave is established in a snakey as shown in the diagram at the right. The distance from point A to point B is known to be 4.69 meters. When not being vibrated as a standing wave, a single pulse introduced into the medium at point A will travel to the opposite end and back in 2.70 seconds.

  7. Oscillations and Simple Harmonic Motion: Problems 2

    Problem : A mass of 2 kg is attached to a spring with constant 18 N/m. It is then displaced to the point x = 2. How much time does it take for the block to travel to the point x = 1 ? For this problem we use the sin and cosine equations we derived for simple harmonic motion. Recall that x = xmcos (σt).

  8. PDF Solutions 3: Damped and Forced Oscillators (Midterm Week)

    Solutions 3: Damped and Forced Oscillators (Midterm Week) Preface: This problem set provides practice in understanding damped harmonic oscillator systems, solving forced oscillator equations, and exploring numerical solutions to di erential equations. Given the information in the prompt and in the plot we want to determine the mass of the oscil ...

  9. 15.S: Oscillations (Summary)

    15.6 Forced Oscillations. A system's natural frequency is the frequency at which the system oscillates if not affected by driving or damping forces. A periodic force driving a harmonic oscillator at its natural frequency produces resonance. The system is said to resonate.

  10. PDF Chapter 15 Oscillatory Motion. Solutions of Selected Problems

    Oscillatory Motion. Solutions of Selected Problems 15.1 Problem 15.18 (In the text book) block-spring system oscillates with an amplitude of 3.50 cm. If the spring constant is 250 N/m and the mass of the block is 0.500 kg, determine the mechanical energy of the system, the maximum speed of the block, and the maximum acceleration. Solution

  11. PDF AP Physics 1- Simple Harmonic Motion and Waves Practice Problems FACT

    Q1. A block oscillating on a spring moves from its position of max spring extension to max compression in 0.25 s. Determine the period and frequency of motion. Q2. A student observing an oscillating block, counts 45.5 cycles of oscillation in one minute. Determine the frequency and period.

  12. Springs & Oscillations Practice Questions

    m. kg. "How much stuff". Gravitational Field Strength. g. m/s 2. Gravitational pull per unit mass. Proceed To Questions. Interactive Springs & Oscillations practice problems: students get instant feedback, automatic homework grading, see results on dashboard.

  13. Simple harmonic motion and rotational motion

    Quiz Unit test About this unit Let's swing, buzz and rotate into the study of simple harmonic and rotational motion! Learn about the period and energy associated with a simple harmonic oscillator and the specific kinematic features of rotational motion. Period of simple harmonic oscillators Learn Period of a Pendulum

  14. Learn AP Physics

    Simple harmonic oscillation is exhibited in many natural systems. In introductory physics, one typically focuses on mass-spring and pendulum systems. Oscillatory Motion Video Lessons Harmonic Motion (Mechanical Universe, Episode 16) Resonance (Mechanical Universe, Episode 17) Waves (Mechanical Universe, Episode 18) Multiple-Choice Practice Problems

  15. Unit 6 Overview: Oscillations

    : A type of periodic motion in which the restoring force is proportional to the displacement from equilibrium position and acts in the opposite direction to the displacement. Oscillation: The back-and-forth motion of an object about its equilibrium position. Amplitude: The maximum displacement of an oscillating object from its equilibrium position.

  16. Exams

    Exams. Midterm Exam Solutions (PDF) Final Exam (Individual) (PDF) Final Exam (Group) (PDF) Final Exam (Individual and Group) Solutions (PDF) Course Info. Instructor. Dr. Mobolaji Williams. Departments.

  17. Learn AP Physics

    Resonance (Mechanical Universe, Episode 17) Waves (Mechanical Universe, Episode 18) Multiple-Choice Practice Problems Scroll down to see multiple choice practice problems in oscillation.

  18. Solved Example Problems for Physics: Oscillations

    Solution Earth is assumed to be a homogeneous sphere. Its centre is at O and Radius = R The hole is bored straight through the centre along its diameter. The acceleration due to gravity at the surface of the earth = g Mass of the body dropped inside the hole = m After time t, the depth it reached (inside the earth) = d

  19. Final Exam

    Practice Exams. Final Exam Formula Sheet (PDF) Practice Final Exam 1 (PDF) Practice Final Exam 2 (PDF - 1.3MB) Practice Final Exam 3 (PDF) « Previous | Next ». This section includes information about the final course exam, including exam and solutions files.

  20. Oscillations Practice Problems

    6 ² = 2𝕥² As 𝔔² is constant, 6 acceleration ∝ 2𝕥 Since acceleration is directly proportional to the displacement and acts in a direction opposite to the displacement, the motion of the particle is S.H. ii) As particle performs S.H., we can write the displacement 𝕥 = 𝔴 sin 𝔴 sin𝔔𝕡. cos𝔑 2 sin𝔔𝕡 + 𝔴 cos𝔔𝕡. sin 𝔑 2 Ā cos𝔔𝕡 = 0 vanish separately i. if

  21. PDF Oscillations

    OSCILLATIONS † We can study it. That it, we can solve for the motion exactly. There are many problems in physics that are extremely di-cult or impossible to solve, so we might as well take advantage of a problem we can actually get a handle on. † It is ubiquitous in nature (at least approximately). It holds in an exact sense for

  22. The Calculator Pad: Simple Harmonic Motion Problem Sets

    Problem Set SHM3: Analyzing Position-, Velocity-, and Acceleration-Time Graphs. Relate the position, velocity, acceleration, and time values for a mass vibrating on a horizontal spring. Includes 3 multi-part problems. Problem Set SHM4: Analysis of a Vertical Spring System. Analyze a vertical spring system to determine a variety of values ...