Question 1

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 2

Five particles undergo damped harmonic motion.Values for the spring constant k, the damping constant b, and the mass m are given below.Which leads to the smallest rate of loss of mechanical energy?

Accepted Answer

A) k = 100 N/m, m = 50 g, b = 8 g∙m/s 
B) k = 150 N/m, m = 50 g, b = 5 g∙m/s 
C) k = 150 N/m, m = 10 g, b = 8 g∙m/s 
D) k = 200 N/m, m = 8 g, b = 6 g∙m/s 
E) k = 100 N/m, m = 2 g, b = 4 g∙m/s 
A) k = 100 N/m, m = 50 g, b = 8 g∙m/s 
B) k = 150 N/m, m = 50 g, b = 5 g∙m/s 
C) k = 150 N/m, m = 10 g, b = 8 g∙m/s 
D) k = 200 N/m, m = 8 g, b = 6 g∙m/s 
E) k = 100 N/m, m = 2 g, b = 4 g∙m/s

Question 3

A weight suspended from an ideal spring oscillates up and down with a period T.If the amplitude of the oscillation is doubled, the period will be:

Accepted Answer

A) T 
B) 1.5 T 
C) 2T 
D) T/2 
E) 4T 
A) T 
B) 1.5 T 
C) 2T 
D) T/2 
E) 4T

Question 4

A simple pendulum of length L and mass M has frequency f.To increase its frequency to 2f:

Accepted Answer

A) increase its length to 4L 
B) increase its length to 2L 
C) decrease its length to L/2 
D) decrease its length to L/4 
E) decrease its mass to < M/4 
A) increase its length to 4L 
B) increase its length to 2L 
C) decrease its length to L/2 
D) decrease its length to L/4 
E) decrease its mass to < M/4

Question 5

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 amplitude of the oscillation is:

Accepted Answer

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

Question 6

In simple harmonic motion, the displacement is maximum when the:

Accepted Answer

A) acceleration is zero 
B) velocity is maximum 
C) velocity is zero 
D) kinetic energy is maximum 
E) momentum is maximum 
A) acceleration is zero 
B) velocity is maximum 
C) velocity is zero 
D) kinetic energy is maximum 
E) momentum is maximum

Question 7

A simple pendulum consists of a small ball tied to a string and set in oscillation.As the pendulum swings the tension in the string is:

Accepted Answer

A) constant 
B) a sinusoidal function of time 
C) the square of a sinusoidal function of time 
D) the reciprocal of a sinusoidal function of time 
E) none of the above 
A) constant 
B) a sinusoidal function of time 
C) the square of a sinusoidal function of time 
D) the reciprocal of a sinusoidal function of time 
E) none of the above

Question 8

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 9

A particle is in simple harmonic motion with period T.At time t = 0 it is at the equilibrium point.At the times listed below it is at various points in its cycle.Which of them is farthest away from the equilibrium point?

Accepted Answer

A) 0.5T 
B) 0.7T 
C) T 
D) 1.4T 
E) 1.5T 
A) 0.5T 
B) 0.7T 
C) T 
D) 1.4T 
E) 1.5T

Question 10

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 11

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 12

A particle oscillating in simple harmonic motion is:

Accepted Answer

A) never in equilibrium because it is in motion 
B) never in equilibrium because there is a force 
C) in equilibrium at the ends of its path because its velocity is zero there 
D) in equilibrium at the center of its path because the acceleration is zero there 
E) in equilibrium at the ends of its path because the acceleration is zero there 
A) never in equilibrium because it is in motion 
B) never in equilibrium because there is a force 
C) in equilibrium at the ends of its path because its velocity is zero there 
D) in equilibrium at the center of its path because the acceleration is zero there 
E) in equilibrium at the ends of its path because the acceleration is zero there

Question 13

For an oscillator subjected to a damping force proportional to its velocity:

Accepted Answer

A) the displacement is a sinusoidal function of time 
B) the velocity is a sinusoidal function of time 
C) the frequency is a decreasing function of time 
D) the mechanical energy is constant 
E) none of the above is true 
A) the displacement is a sinusoidal function of time 
B) the velocity is a sinusoidal function of time 
C) the frequency is a decreasing function of time 
D) the mechanical energy is constant 
E) none of the above is true

Question 14

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 15

Frequency f and angular frequency     are related by

Accepted Answer

A) f =  
B) f =   
C) f =   
D) f =  
E) f =   
A) f =  
B) f =   
C) f =   
D) f =  
E) f =

Question 16

A simple pendulum is suspended from the ceiling of an elevator.The elevator is accelerating upwards with acceleration a.The period of this pendulum, in terms of its length L, g and a is:

Accepted Answer

A)    
B)    
C)    
D)    
E)    
A)    
B)    
C)    
D)    
E)

Question 17

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 18

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 19

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 20

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

Exam 15: Oscillations

In simple harmonic motion:

Five particles undergo damped harmonic motion.Values for the spring constant k, the damping constant b, and the mass m are given below.Which leads to the smallest rate of loss of mechanical energy?

A weight suspended from an ideal spring oscillates up and down with a period T.If the amplitude of the oscillation is doubled, the period will be:

A simple pendulum of length L and mass M has frequency f.To increase its frequency to 2f:

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 amplitude of the oscillation is:

In simple harmonic motion, the displacement is maximum when the:

A simple pendulum consists of a small ball tied to a string and set in oscillation.As the pendulum swings the tension in the string is:

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:

A particle is in simple harmonic motion with period T.At time t = 0 it is at the equilibrium point.At the times listed below it is at various points in its cycle.Which of them is farthest away from the equilibrium point?

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:

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 oscillating in simple harmonic motion is:

For an oscillator subjected to a damping force proportional to its velocity:

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:

Frequency f and angular frequency are related by

A simple pendulum is suspended from the ceiling of an elevator.The elevator is accelerating upwards with acceleration a.The period of this pendulum, in terms of its length L, g and a is:

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

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

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:

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:

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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:

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

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: