Question 1

The amplitude of any oscillator will be doubled by:

Accepted Answer

A) doubling only the initial displacement 
B) doubling only the initial speed 
C) doubling the initial displacement and halving the initial speed 
D) doubling the initial speed and halving the initial displacement 
E) doubling both the initial displacement and the initial speed 
A) doubling only the initial displacement 
B) doubling only the initial speed 
C) doubling the initial displacement and halving the initial speed 
D) doubling the initial speed and halving the initial displacement 
E) doubling both the initial displacement and the initial speed

Question 2

A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it.The angular frequency of this mass-spring system:

Accepted Answer

A) is 0.088 rad/s 
B) is 33 rad/s 
C) is 200 rad/s 
D) is 1140 rad/s 
E) cannot be computed unless the value of M is given 
A) is 0.088 rad/s 
B) is 33 rad/s 
C) is 200 rad/s 
D) is 1140 rad/s 
E) cannot be computed unless the value of M is given

Question 3

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 4

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 5

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

Accepted Answer

A) 0.79 rad/s 
B) 1.57 rad/s 
C) 2.0 rad/s 
D) 6.3 rad/s 
E) 12.6 rad/s 
A) 0.79 rad/s 
B) 1.57 rad/s 
C) 2.0 rad/s 
D) 6.3 rad/s 
E) 12.6 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 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 7

In simple harmonic motion:

Accepted Answer

A) the acceleration is greatest at the maximum displacement 
B) the velocity is greatest at the maximum displacement 
C) the period depends on the amplitude 
D) the acceleration is constant 
E) the acceleration is greatest at zero displacement 
A) the acceleration is greatest at the maximum displacement 
B) the velocity is greatest at the maximum displacement 
C) the period depends on the amplitude 
D) the acceleration is constant 
E) the acceleration is greatest at zero displacement

Question 8

The period of a simple pendulum is 1 s on Earth.When brought to a planet where g is one-tenth that on Earth, its period becomes:

Accepted Answer

A) 1 s 
B)   s 
C) 1/10 s 
D)  s 
E) 10 s 
A) 1 s 
B)   s 
C) 1/10 s 
D)  s 
E) 10 s

Question 9

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, its total energy is:

Accepted Answer

A) 0 J 
B) 3 J 
C) 4 J 
D) 5 J 
E) 8 J 
A) 0 J 
B) 3 J 
C) 4 J 
D) 5 J 
E) 8 J

Question 10

The amplitude and phase constant of an oscillator are determined by:

Accepted Answer

A) the frequency 
B) the angular frequency 
C) the initial displacement alone 
D) the initial velocity alone 
E) both the initial displacement and velocity 
A) the frequency 
B) the angular frequency 
C) the initial displacement alone 
D) the initial velocity alone 
E) both the initial displacement and velocity

Question 11

If the length of a simple pendulum is doubled, its period will:

Accepted Answer

A) halve 
B) increase by a factor of 
C) decrease by a factor of 
D) double 
E) remain the same 
A) halve 
B) increase by a factor of 
C) decrease by a factor of 
D) double 
E) remain the same

Question 12

Frequency f and angular frequency  $ \omega $ are related by

Accepted Answer

A) f =  $\pi$ $ \omega $ 
B) f = 2 $\pi$ $ \omega $ 
C) f =  $ \omega $/ $\pi$ 
D) f =  $ \omega $/2 $\pi$ 
E) f = 2 $ \omega $/ $\pi$ 
A) f =  $\pi$ $ \omega $ 
B) f = 2 $\pi$ $ \omega $ 
C) f =  $ \omega $/ $\pi$ 
D) f =  $ \omega $/2 $\pi$ 
E) f = 2 $ \omega $/ $\pi$

Question 13

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 14

Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums.The masses and radii are   Order the hoops according to the periods of their motions, smallest to largest.

Accepted Answer

A) 1, 2, 3, 4, 5 
B) 5, 4, 3, 2, 1 
C) 1, 2, 3, 5, 4 
D) 1, 2, 5, 4, 3 
E) 5, 4, 1, 2, 3 
A) 1, 2, 3, 4, 5 
B) 5, 4, 3, 2, 1 
C) 1, 2, 3, 5, 4 
D) 1, 2, 5, 4, 3 
E) 5, 4, 1, 2, 3

Question 15

A sinusoidal force with a given amplitude is applied to an oscillator.To maintain the largest amplitude oscillation the frequency of the applied force should be:

Accepted Answer

A) half the natural frequency of the oscillator 
B) the same as the natural frequency of the oscillator 
C) twice the natural frequency of the oscillator 
D) unrelated to the natural frequency of the oscillator 
E) determined from the maximum speed desired 
A) half the natural frequency of the oscillator 
B) the same as the natural frequency of the oscillator 
C) twice the natural frequency of the oscillator 
D) unrelated to the natural frequency of the oscillator 
E) determined from the maximum speed desired

Question 16

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m.If the system has an energy of 6.0 J, then the maximum speed of the block is:

Accepted Answer

A) 0.06 m/s 
B) 0.17 m/s 
C) 0.24 m/s 
D) 4.9 m/s 
E) 6.9 m/s 
A) 0.06 m/s 
B) 0.17 m/s 
C) 0.24 m/s 
D) 4.9 m/s 
E) 6.9 m/s

Question 17

The amplitude of oscillation of a simple pendulum is increased from 1$\degree$ to 4$\degree$.Its maximum acceleration changes by a factor of:

Accepted Answer

A) 1/4 
B) 1/2 
C) 2 
D) 4 
E) 16 
A) 1/4 
B) 1/2 
C) 2 
D) 4 
E) 16

Question 18

A particle moves in simple harmonic motion according to x = 2cos(50t), where x is in meters and t is in seconds.Its maximum velocity is:

Accepted Answer

A) 100 sin(50t)m/s 
B) 100 cos(50t)m/s 
C) 100 m/s 
D) 200 m/s 
E) none of these 
A) 100 sin(50t)m/s 
B) 100 cos(50t)m/s 
C) 100 m/s 
D) 200 m/s 
E) none of these

Question 19

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 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

The amplitude of any oscillator will be doubled by:

A certain spring elongates 9 mm when it is suspended vertically and a block of mass M is hung on it.The angular frequency of this mass-spring system:

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:

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 angular frequency is:

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?

In simple harmonic motion:

The period of a simple pendulum is 1 s on Earth.When brought to a planet where g is one-tenth that on Earth, its period becomes:

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, its total energy is:

The amplitude and phase constant of an oscillator are determined by:

If the length of a simple pendulum is doubled, its period will:

Frequency f and angular frequency ω \omega ω are related by

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?

Five hoops are each pivoted at a point on the rim and allowed to swing as physical pendulums.The masses and radii are Order the hoops according to the periods of their motions, smallest to largest.

A sinusoidal force with a given amplitude is applied to an oscillator.To maintain the largest amplitude oscillation the frequency of the applied force should be:

A 0.25-kg block oscillates on the end of the spring with a spring constant of 200 N/m.If the system has an energy of 6.0 J, then the maximum speed of the block is:

The amplitude of oscillation of a simple pendulum is increased from 1 °\degree° to 4 °\degree° .Its maximum acceleration changes by a factor of:

A particle moves in simple harmonic motion according to x = 2cos(50t), where x is in meters and t is in seconds.Its maximum velocity is:

An oscillatory motion must be simple harmonic if:

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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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:

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 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, its total energy is:

Frequency f and angular frequency $\omega$ are related by

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?

The amplitude of oscillation of a simple pendulum is increased from 1 $\degree$ to 4 $\degree$ .Its maximum acceleration changes by a factor of:

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: