Question 1

This plot shows a mass oscillating as x = xm cos (ωt + φ). What are xm and φ?

Accepted Answer

A)  1 m, 0° 
B)  2 m, 0° 
C)  2 m, 90° 
D)  4 m, 0° 
E)  4 m, 90° 
A)  1 m, 0° 
B)  2 m, 0° 
C)  2 m, 90° 
D)  4 m, 0° 
E)  4 m, 90°

Question 2

A meter stick is pivoted at a point a distance a from its center and swings as a physical pendulum. Of the following values for a, which results in the shortest period of oscillation?

Accepted Answer

A)  a = 0.1 m 
B)  a = 0.2 m 
C)  a = 0.3 m 
D)  a = 0.4 m 
E)  a = 0.5 m 
A)  a = 0.1 m 
B)  a = 0.2 m 
C)  a = 0.3 m 
D)  a = 0.4 m 
E)  a = 0.5 m

Question 3

An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is v0 and in the second it is 4v0. In the second trial:

Accepted Answer

A)  the amplitude is half as great and the maximum acceleration is twice as great 
B)  the amplitude is twice as great and the maximum acceleration is half as great 
C)  both the amplitude and the maximum acceleration are twice as great 
D)  both the amplitude and the maximum acceleration are four times as great 
E)  the amplitude is four times as great and the maximum acceleration is twice as great 
A)  the amplitude is half as great and the maximum acceleration is twice as great 
B)  the amplitude is twice as great and the maximum acceleration is half as great 
C)  both the amplitude and the maximum acceleration are twice as great 
D)  both the amplitude and the maximum acceleration are four times as great 
E)  the amplitude is four times as great and the maximum acceleration is twice as great

Question 4

An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its frequency is:

Accepted Answer

A)  2 Hz 
B)  10 s 
C)  0.05 Hz 
D)  2 s 
E)  0.50 s 
A)  2 Hz 
B)  10 s 
C)  0.05 Hz 
D)  2 s 
E)  0.50 s

Question 5

At the instant its angular displacement is 0.32 rad, the angular acceleration of a physical pendulum is -630 rad/s2. What is its angular frequency of oscillation?

Accepted Answer

A)  6.6 rad/s 
B)  14 rad/s 
C)  20 rad/s 
D)  44 rad/s 
E)  200 rad/s 
A)  6.6 rad/s 
B)  14 rad/s 
C)  20 rad/s 
D)  44 rad/s 
E)  200 rad/s

Question 6

A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the amplitude of the motion at t = 5.0 s?

Accepted Answer

A)  1.5 m 
B)  1.3 m 
C)  1.0 m 
D)  0.67 m 
E)  0.24 m 
A)  1.5 m 
B)  1.3 m 
C)  1.0 m 
D)  0.67 m 
E)  0.24 m

Question 7

An oscillator is driven by a sinusoidal force. The frequency of the applied force:

Accepted Answer

A)  must be equal to the natural frequency of the oscillator 
B)  becomes the natural frequency of the oscillator 
C)  must be less than the natural frequency of the oscillator 
D)  must be greater than the natural frequency of the oscillator 
E)  is independent of the natural frequency of the oscillator 
A)  must be equal to the natural frequency of the oscillator 
B)  becomes the natural frequency of the oscillator 
C)  must be less than the natural frequency of the oscillator 
D)  must be greater than the natural frequency of the oscillator 
E)  is independent of the natural frequency of the oscillator

Question 8

A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by:

Accepted Answer

A)  the damping force 
B)  the initial amplitude 
C)  the initial velocity 
D)  the force of gravity 
E)  none of the above 
A)  the damping force 
B)  the initial amplitude 
C)  the initial velocity 
D)  the force of gravity 
E)  none of the above

Question 9

An oscillator is subjected to a damping force that is proportional to its velocity. A sinusoidal force is applied to it. After a long time:

Accepted Answer

A)  its amplitude is an increasing function of time 
B)  its amplitude is a decreasing function of time 
C)  its amplitude is constant 
D)  its amplitude is a decreasing function of time only if the damping constant is large 
E)  its amplitude increases over some portions of a cycle and decreases over other portions 
A)  its amplitude is an increasing function of time 
B)  its amplitude is a decreasing function of time 
C)  its amplitude is constant 
D)  its amplitude is a decreasing function of time only if the damping constant is large 
E)  its amplitude increases over some portions of a cycle and decreases over other portions

Question 10

A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = -1/2 xm, the kinetic and potential energies are:

Accepted Answer

A)  K = 6 J and U = 2 J 
B)  K = 6 J and U = -2 J 
C)  K = 8 J and U = 0 J 
D)  K = 0 J and U = 8 J 
E)  K = 0 J and U = -8 J 
A)  K = 6 J and U = 2 J 
B)  K = 6 J and U = -2 J 
C)  K = 8 J and U = 0 J 
D)  K = 0 J and U = 8 J 
E)  K = 0 J and U = -8 J

Question 11

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the maximum speed of the block is:

Accepted Answer

A)  0.13 m/s 
B)  0.18 m/s 
C)  3.7 m/s 
D)  5.2 m/s 
E)  13 m/s 
A)  0.13 m/s 
B)  0.18 m/s 
C)  3.7 m/s 
D)  5.2 m/s 
E)  13 m/s

Question 12

When a body executes simple harmonic motion, its acceleration at the ends of its path must be:

Accepted Answer

A)  zero 
B)  less than g 
C)  more than g 
D)  suddenly changing in sign 
E)  none of these 
A)  zero 
B)  less than g 
C)  more than g 
D)  suddenly changing in sign 
E)  none of these

Question 13

Below are sets of values for the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion. Which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?

Accepted Answer

The answer of Below are sets of values for the...

Question 14

A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When its kinetic energy is 8 J, it is at:

Accepted Answer

A)  x = 0 
B)  x = x1 
C)  x = xm/2 
D)  x = xm/   
E)  x = xm 
A)  x = 0 
B)  x = x1 
C)  x = xm/2 
D)  x = xm/   
E)  x = xm

Question 15

Which of the following is the difference between a simple pendulum and a physical pendulum?

Accepted Answer

A)  The physical pendulum does not rotate around its center of mass. 
B)  The physical pendulum does not depend on the acceleration of gravity. 
C)  The physical pendulum has an extended mass. 
D)  The simple pendulum has a small amplitude. 
E)  The physical pendulum rotates around its center of mass. 
A)  The physical pendulum does not rotate around its center of mass. 
B)  The physical pendulum does not depend on the acceleration of gravity. 
C)  The physical pendulum has an extended mass. 
D)  The simple pendulum has a small amplitude. 
E)  The physical pendulum rotates around its center of mass.

Question 16

A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the particle's position at t = 5.0 s?

Accepted Answer

A)  -1.5 m 
B)  -0.73 m 
C)  0 m 
D)  0.73 m 
E)  1.5 m 
A)  -1.5 m 
B)  -0.73 m 
C)  0 m 
D)  0.73 m 
E)  1.5 m

Question 17

An oscillatory motion must be simple harmonic if:

Accepted Answer

A)  the amplitude is small 
B)  the potential energy is equal to the kinetic energy 
C)  the motion is along the arc of a circle 
D)  the acceleration varies sinusoidally with time 
E)  the derivative, dU/dx, of the potential energy is negative 
A)  the amplitude is small 
B)  the potential energy is equal to the kinetic energy 
C)  the motion is along the arc of a circle 
D)  the acceleration varies sinusoidally with time 
E)  the derivative, dU/dx, of the potential energy is negative

Question 18

A disk whose rotational inertia is 450 kg∙m2 hangs from a wire whose torsion constant is 2300 N∙m/rad. What is the angular frequency of its torsional oscillations?

Accepted Answer

A)  0.20 rad/s 
B)  0.44 rad/s 
C)  1.0 rad/s 
D)  2.3 rad/s 
E)  5.1 rad/s 
A)  0.20 rad/s 
B)  0.44 rad/s 
C)  1.0 rad/s 
D)  2.3 rad/s 
E)  5.1 rad/s

Question 19

The acceleration of a body executing simple harmonic motion leads the velocity by what phase?

Accepted Answer

A)  0 rad 
B)   $\pi$/8 rad 
C)   $\pi$/4 rad 
D)   $\pi$/2 rad 
E)   $\pi$ rad 
A)  0 rad 
B)   $\pi$/8 rad 
C)   $\pi$/4 rad 
D)   $\pi$/2 rad 
E)   $\pi$ rad

Question 20

A particle moves back and forth along the x axis from x = -xm to x = +xm, in simple harmonic motion with period T. At time t = 0 it is at x = +xm. When t = 0.75T:

Accepted Answer

A)  it is at x = 0 and is traveling toward x = +xm 
B)  it is at x = 0 and is traveling toward x = -xm 
C)  it is at x = +xm and is at rest 
D)  it is between x = 0 and x = +xm and is traveling toward x = -xm 
E)  it is between x = 0 and x = -xm and is traveling toward x = -xm 
A)  it is at x = 0 and is traveling toward x = +xm 
B)  it is at x = 0 and is traveling toward x = -xm 
C)  it is at x = +xm and is at rest 
D)  it is between x = 0 and x = +xm and is traveling toward x = -xm 
E)  it is between x = 0 and x = -xm and is traveling toward x = -xm

Exam 15: Oscillations

This plot shows a mass oscillating as x = xm cos (ωt + φ). What are xm and φ?

A meter stick is pivoted at a point a distance a from its center and swings as a physical pendulum. Of the following values for a, which results in the shortest period of oscillation?

An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is v0 and in the second it is 4v0. In the second trial:

An object attached to one end of a spring makes 20 vibrations in 10 seconds. Its frequency is:

At the instant its angular displacement is 0.32 rad, the angular acceleration of a physical pendulum is -630 rad/s2. What is its angular frequency of oscillation?

A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the amplitude of the motion at t = 5.0 s?

An oscillator is driven by a sinusoidal force. The frequency of the applied force:

A sinusoidal force with a given amplitude is applied to an oscillator. At resonance the amplitude of the oscillation is limited by:

An oscillator is subjected to a damping force that is proportional to its velocity. A sinusoidal force is applied to it. After a long time:

A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = -1/2 xm, the kinetic and potential energies are:

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m. If the oscillation is started by elongating the spring 0.15 m and giving the block a speed of 3.0 m/s, then the maximum speed of the block is:

When a body executes simple harmonic motion, its acceleration at the ends of its path must be:

Below are sets of values for the spring constant k, damping constant b, and mass m for a particle in damped harmonic motion. Which of the sets takes the longest time for its mechanical energy to decrease to one-fourth of its initial value?

A particle is in simple harmonic motion along the x axis. The amplitude of the motion is xm. When it is at x = x1, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When its kinetic energy is 8 J, it is at:

Which of the following is the difference between a simple pendulum and a physical pendulum?

A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the particle's position at t = 5.0 s?

An oscillatory motion must be simple harmonic if:

A disk whose rotational inertia is 450 kg∙m2 hangs from a wire whose torsion constant is 2300 N∙m/rad. What is the angular frequency of its torsional oscillations?

The acceleration of a body executing simple harmonic motion leads the velocity by what phase?

A particle moves back and forth along the x axis from x = -xm to x = +xm, in simple harmonic motion with period T. At time t = 0 it is at x = +xm. When t = 0.75T:

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This plot shows a mass oscillating as x = x_m cos (ωt + φ). What are x_m and φ?

An object on the end of a spring is set into oscillation by giving it an initial velocity while it is at its equilibrium position. In the first trial the initial velocity is v₀ and in the second it is 4v₀. In the second trial:

At the instant its angular displacement is 0.32 rad, the angular acceleration of a physical pendulum is -630 rad/s². What is its angular frequency of oscillation?

A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10^-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the amplitude of the motion at t = 5.0 s?

A particle is in simple harmonic motion along the x axis. The amplitude of the motion is x_m. When it is at x = x₁, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When it is at x = -1/2 x_m, the kinetic and potential energies are:

A particle is in simple harmonic motion along the x axis. The amplitude of the motion is x_m. When it is at x = x₁, its kinetic energy is K = 5 J and its potential energy (measured with U = 0 at x = 0) is U = 3 J. When its kinetic energy is 8 J, it is at:

A particle undergoes damped harmonic motion. The spring constant is 100 N/m; the damping constant is 8.0 x 10^-3 kg∙m/s, and the mass is 0.050 kg. If the particle starts at its maximum displacement, x = 1.5 m, at time t = 0, what is the particle's position at t = 5.0 s?

A disk whose rotational inertia is 450 kg∙m² hangs from a wire whose torsion constant is 2300 N∙m/rad. What is the angular frequency of its torsional oscillations?

A particle moves back and forth along the x axis from x = -x_m to x = +x_m, in simple harmonic motion with period T. At time t = 0 it is at x = +x_m. When t = 0.75T: