Question 1

A mass of 0.150 kg is attached to a spring with a force constant of 3.58 N/m and undergoes simple harmonic oscillations. What is the period of the oscillations?

Accepted Answer

A)  2.57 s 
B)  0.527 s 
C)  0.263 s 
D)  1.14 s 
E)  1.29 s 
A)  2.57 s 
B)  0.527 s 
C)  0.263 s 
D)  1.14 s 
E)  1.29 s

Question 2

Why are troops instructed to break step when they are marching over a bridge?

Accepted Answer

If all the soldiers march in step,a sing

Question 3

An underdamped spring-mass system consists of a spring with a force constant of 2.00 N/m and a mass of 550 g. It is observed that the oscillations decrease in magnitude by 10.0% every 360 s. What is the value of the damping constant for the system?

Accepted Answer

A)  3.22 × 10-4 Ns/m 
B)  2.16 × 10-4 Ns/m 
C)  11.7 × 10-4 Ns/m 
D)  5.85 × 10-4 Ns/m 
E)  8.95 × 10-4 Ns/m 
A)  3.22 × 10-4 Ns/m 
B)  2.16 × 10-4 Ns/m 
C)  11.7 × 10-4 Ns/m 
D)  5.85 × 10-4 Ns/m 
E)  8.95 × 10-4 Ns/m

Question 4

When the mass of a simple pendulum is tripled, the time required for one complete vibration

Accepted Answer

A)  increases by a factor of 2. 
B)  increases by a factor of 3. 
C)  does not change. 
D)  decreases to one-third of its original value. 
E)  decreases to 1/   of its original value. 
A)  increases by a factor of 2. 
B)  increases by a factor of 3. 
C)  does not change. 
D)  decreases to one-third of its original value. 
E)  decreases to 1/   of its original value.

Question 5

A mass is oscillating on a spring with a period of 4.60 s. At t = 0 s the mass has zero speed and is at x = 8.30 cm. What is the value of t the first time after t = 0 s that the mass is at x = 4.15 cm?

Accepted Answer

A)  0.575 s 
B)  0.767 s 
C)  1.15 s 
D)  1.30 s 
E)  1.53 s 
A)  0.575 s 
B)  0.767 s 
C)  1.15 s 
D)  1.30 s 
E)  1.53 s

Question 6

When a mass of 0.350 kg is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The mass is now displaced from its equilibrium position and undergoes simple harmonic oscillations. What is the period of the oscillations?

Accepted Answer

A)  0.695 s 
B)  0.483 s 
C)  0.286 s 
D)  0.0769 s 
E)  1.44 s 
A)  0.695 s 
B)  0.483 s 
C)  0.286 s 
D)  0.0769 s 
E)  1.44 s

Question 7

A spring with a force constant of 1.50 N/m is attached to a mass of 120 g. The system has a damping constant of 0.0180 Ns/m. How long does it take the amplitude of the oscillations to decrease from 10.0 mm to 5.00 mm?

Accepted Answer

A)  12.5 s 
B)  10.0 s 
C)  6.25 s 
D)  4.62 s 
E)  9.24 s 
A)  12.5 s 
B)  10.0 s 
C)  6.25 s 
D)  4.62 s 
E)  9.24 s

Question 8

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration?

Accepted Answer

A)  The period does not change. 
B)  The period increases. 
C)  The period decreases. 
D)  The period becomes zero. 
E)  The period decreases if the downward acceleration is more than g/2 but increases if the downward acceleration is less than g/2. 
A)  The period does not change. 
B)  The period increases. 
C)  The period decreases. 
D)  The period becomes zero. 
E)  The period decreases if the downward acceleration is more than g/2 but increases if the downward acceleration is less than g/2.

Question 9

How much work is required to stretch a spring 25.2 cm if its force constant is 12.3 N/m?

Accepted Answer

A)  0.391 J 
B)  0.488 J 
C)  3.10 J 
D)  1.05 J 
E)  0.381 J 
A)  0.391 J 
B)  0.488 J 
C)  3.10 J 
D)  1.05 J 
E)  0.381 J

Question 10

The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46 s-1)t]. Write an expression for the velocity of the particle as a function of time.

Accepted Answer

-(95.0 cm/

Question 11

A mass is attached to a spring and oscillates with a period T. If the mass is doubled, what is the new period?

Accepted Answer

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

Question 12

The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46 s-1)t]. What is the angular frequency for this motion?

Accepted Answer

A)  0.183 rad/s 
B)  5.46 rad/s 
C)  2.34 rad/s 
D)  17.4 rad/s 
E)  0.869 rad/s 
A)  0.183 rad/s 
B)  5.46 rad/s 
C)  2.34 rad/s 
D)  17.4 rad/s 
E)  0.869 rad/s

Question 13

A child and an adult are walking. Their legs swing like physical pendulums and both swing through the same maximum angle. The adult is 1.5 times as tall as the child, and all their dimensions are scaled proportionately. They also have the same mass per unit volume. How many steps does the child take in the time that the adult takes 49 steps?

Accepted Answer

The answer of A child and an adult are walking....

Question 14

In a supermarket, you place a 5 lb (22.3 N) bag of oranges on a scale. The scale starts to oscillate at 2.70 Hz. What is the force constant of the scale?

Accepted Answer

A)  654 N/m 
B)  602 N/m 
C)  327 N/m 
D)  819 N/m 
E)  409 N/m 
A)  654 N/m 
B)  602 N/m 
C)  327 N/m 
D)  819 N/m 
E)  409 N/m

Question 15

An astronaut has landed on an asteroid and conducts an experiment to determine the acceleration of gravity on that asteroid. She uses a pendulum that has a period of oscillation of 2.00 s on Earth and finds that on the asteroid the period is 11.3 s. What is the acceleration of gravity on that asteroid?

Accepted Answer

A)  0.307 m/s2 
B)  1.66 m/s2 
C)  1.74 m/s2 
D)  5.51 m/s2 
E)  0.0544 m/s2 
A)  0.307 m/s2 
B)  1.66 m/s2 
C)  1.74 m/s2 
D)  5.51 m/s2 
E)  0.0544 m/s2

Question 16

A pendulum that was originally erected by Foucault at the Pantheon in Paris for the Paris Exhibition in 1851 was restored in 1995. It has a 28.0 kg sphere suspended from a 67.0-m light cable. If the amplitude of the swing is 5.00 m, what is the maximum speed of the sphere?

Accepted Answer

A)  3.57 m/s 
B)  3.65 m/s 
C)  13.1 m/s 
D)  4.16 m/s 
E)  1.91 m/s 
A)  3.57 m/s 
B)  3.65 m/s 
C)  13.1 m/s 
D)  4.16 m/s 
E)  1.91 m/s

Question 17

An astronaut has landed on another planet and conducts an experiment to determine the acceleration of gravity on that planet. She uses a pendulum 0.640 m long and determines that the period of oscillation is 2.60 s. What is the acceleration of gravity on that planet?

Accepted Answer

A)  4.85 m/s2 
B)  1.66 m/s2 
C)  3.74 m/s2 
D)  2.39 m/s2 
E)  9.81 m/s2 
A)  4.85 m/s2 
B)  1.66 m/s2 
C)  3.74 m/s2 
D)  2.39 m/s2 
E)  9.81 m/s2

Question 18

A simple harmonic oscillator is undergoing oscillations with an amplitude A. How far is it from its equilibrium position when the kinetic and potential energies are equal?

Accepted Answer

A)  A/2 
B)  A/   
C)  A 
D)  A/3 
E)  A/   
A)  A/2 
B)  A/   
C)  A 
D)  A/3 
E)  A/

Question 19

You have connected a loudspeaker that is facing upwards to a variable frequency source and notice that a small screw has fallen into the loudspeaker. As you increase the frequency of the signal you notice that at a frequency of 20.0 Hz the screw no longer moves with the speaker but starts to leave the surface of the speaker intermittently. What must be the amplitude of the oscillations?

Accepted Answer

A)  0.621 mm 
B)  2.45 mm 
C)  1.60 mm 
D)  0.893 mm 
E)  0.200 mm 
A)  0.621 mm 
B)  2.45 mm 
C)  1.60 mm 
D)  0.893 mm 
E)  0.200 mm

Question 20

When a mass of 0.350 kg is attached to a vertical spring and lowered slowly, the spring stretches a distance d. The mass is now displaced from its equilibrium position and undergoes 100 oscillations in 48.9 s. What is the stretch distance d?

Accepted Answer

A)  2.35 cm 
B)  2.97 cm 
C)  4.71 cm 
D)  5.94 cm 
E)  6.28 cm 
A)  2.35 cm 
B)  2.97 cm 
C)  4.71 cm 
D)  5.94 cm 
E)  6.28 cm

Exam 13: Oscillations About Equilibrium

A mass of 0.150 kg is attached to a spring with a force constant of 3.58 N/m and undergoes simple harmonic oscillations. What is the period of the oscillations?

Why are troops instructed to break step when they are marching over a bridge?

An underdamped spring-mass system consists of a spring with a force constant of 2.00 N/m and a mass of 550 g. It is observed that the oscillations decrease in magnitude by 10.0% every 360 s. What is the value of the damping constant for the system?

When the mass of a simple pendulum is tripled, the time required for one complete vibration

A mass is oscillating on a spring with a period of 4.60 s. At t = 0 s the mass has zero speed and is at x = 8.30 cm. What is the value of t the first time after t = 0 s that the mass is at x = 4.15 cm?

When a mass of 0.350 kg is attached to a vertical spring and lowered slowly, the spring stretches 12.0 cm. The mass is now displaced from its equilibrium position and undergoes simple harmonic oscillations. What is the period of the oscillations?

A spring with a force constant of 1.50 N/m is attached to a mass of 120 g. The system has a damping constant of 0.0180 Ns/m. How long does it take the amplitude of the oscillations to decrease from 10.0 mm to 5.00 mm?

A pendulum of length L is suspended from the ceiling of an elevator. When the elevator is at rest the period of the pendulum is T. How does the period of the pendulum change when the elevator moves downward with constant acceleration?

How much work is required to stretch a spring 25.2 cm if its force constant is 12.3 N/m?

The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46 s-1)t]. Write an expression for the velocity of the particle as a function of time.

A mass is attached to a spring and oscillates with a period T. If the mass is doubled, what is the new period?

The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46 s-1)t]. What is the angular frequency for this motion?

In a supermarket, you place a 5 lb (22.3 N) bag of oranges on a scale. The scale starts to oscillate at 2.70 Hz. What is the force constant of the scale?

A pendulum that was originally erected by Foucault at the Pantheon in Paris for the Paris Exhibition in 1851 was restored in 1995. It has a 28.0 kg sphere suspended from a 67.0-m light cable. If the amplitude of the swing is 5.00 m, what is the maximum speed of the sphere?

An astronaut has landed on another planet and conducts an experiment to determine the acceleration of gravity on that planet. She uses a pendulum 0.640 m long and determines that the period of oscillation is 2.60 s. What is the acceleration of gravity on that planet?

A simple harmonic oscillator is undergoing oscillations with an amplitude A. How far is it from its equilibrium position when the kinetic and potential energies are equal?

When a mass of 0.350 kg is attached to a vertical spring and lowered slowly, the spring stretches a distance d. The mass is now displaced from its equilibrium position and undergoes 100 oscillations in 48.9 s. What is the stretch distance d?

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The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46 s^-1)t]. Write an expression for the velocity of the particle as a function of time.

The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46 s^-1)t]. What is the angular frequency for this motion?