Question 1

In a grandfather clock, the pendulum measures the time elapsed. A grandfather clock is gaining time. Should you shorten or lengthen the pendulum?

Accepted Answer

You should lengthen

Question 2

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 its acceleration at t = 2.50 s?

Accepted Answer

A)  1.33 cm/s2 
B)  0.784 cm/s2 
C)  11.5 cm/s2 
D)  14.9 cm/s2 
E)  0 cm/s2 
A)  1.33 cm/s2 
B)  0.784 cm/s2 
C)  11.5 cm/s2 
D)  14.9 cm/s2 
E)  0 cm/s2

Question 3

In 1851 Jean Bernard Leon Foucault demonstrated the rotation of the Earth using a pendulum 11.0 m long, which was set up in the Paris Observatory. What was the period of oscillation of the pendulum?

Accepted Answer

A)  6.65 s 
B)  5.63 s 
C)  1.79 s 
D)  2.12 s 
E)  2.58 s 
A)  6.65 s 
B)  5.63 s 
C)  1.79 s 
D)  2.12 s 
E)  2.58 s

Question 4

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. In any 4.60 s time interval, how much time is the mass more than 4.15 cm away from x = 0 cm?

Accepted Answer

A)  0.326 s 
B)  0.575 s 
C)  0.767 s 
D)  1.53 s 
E)  3.07 s 
A)  0.326 s 
B)  0.575 s 
C)  0.767 s 
D)  1.53 s 
E)  3.07 s

Question 5

A mass of 1.53 kg is attached to a spring and the system is undergoing simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. What is the total mechanical energy of the system?

Accepted Answer

A)  0.844 J 
B)  0.646 J 
C)  0.633 J 
D)  0.955 J 
E)  0 J 
A)  0.844 J 
B)  0.646 J 
C)  0.633 J 
D)  0.955 J 
E)  0 J

Question 6

For a periodic process, the number of cycles per unit time is called the

Accepted Answer

A)  amplitude. 
B)  wavelength. 
C)  frequency. 
D)  period. 
E)  energy. 
A)  amplitude. 
B)  wavelength. 
C)  frequency. 
D)  period. 
E)  energy.

Question 7

If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations?

Accepted Answer

A)  4560 Hz 
B)  1450 Hz 
C)  3.98 Hz 
D)  2.54 Hz 
E)  1.27 Hz 
A)  4560 Hz 
B)  1450 Hz 
C)  3.98 Hz 
D)  2.54 Hz 
E)  1.27 Hz

Question 8

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 its speed at t = 2.50 s?

Accepted Answer

A)  10.9 cm/s 
B)  3.06 cm/s 
C)  3.32 cm/s 
D)  1.80 cm/s 
E)  0 cm/s 
A)  10.9 cm/s 
B)  3.06 cm/s 
C)  3.32 cm/s 
D)  1.80 cm/s 
E)  0 cm/s

Question 9

The position of an air-track cart that is oscillating on a spring is given by x = (12.4 cm) cos[(6.35 s-1)t]. At what value of t after t = 0 s is the cart first located at x = 8.47 cm?

Accepted Answer

A)  4.34 s 
B)  0.108 s 
C)  0.129 s 
D)  7.39 s 
E)  7.75 s 
A)  4.34 s 
B)  0.108 s 
C)  0.129 s 
D)  7.39 s 
E)  7.75 s

Question 10

A mass of 1.53 kg is attached to a spring and the system is undergoing simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. What is the speed of the mass when it is 3.00 cm from its equilibrium position?

Accepted Answer

A)  0.0368 m/s 
B)  0.551 m/s 
C)  0.421 m/s 
D)  0.842 m/s 
E)  0.919 m/s 
A)  0.0368 m/s 
B)  0.551 m/s 
C)  0.421 m/s 
D)  0.842 m/s 
E)  0.919 m/s

Question 11

An oscillating system has a small amount of damping. It is observed that in the course of 20.0 s the amplitude has decreased from A to A/2. What additional time is required for the amplitude to decrease to A/4?

Accepted Answer

The answer of An oscillating system has a small amount...

Question 12

FIGURE 13-1  
-Curve B in Figure 13-1 represents

Accepted Answer

A)  an underdamped situation. 
B)  an overdamped situation. 
C)  a moderately damped situation. 
D)  critical damping. 
E)  none of the above 
A)  an underdamped situation. 
B)  an overdamped situation. 
C)  a moderately damped situation. 
D)  critical damping. 
E)  none of the above

Question 13

A mass m is attached to a vertical spring with a force constant k, it oscillates with a period T. If the spring is cut to one third of its original length and the same mass is attached to it, the new period of oscillation will be

Accepted Answer

A)  less than T. 
B)  greater than T. 
C)  equal to T. 
D)  It could be greater or less than T, depending on how you cut the spring. 
A)  less than T. 
B)  greater than T. 
C)  equal to T. 
D)  It could be greater or less than T, depending on how you cut the spring.

Question 14

A vertical spring has a mass hanging from it, which is displaced from the equilibrium position and begins to oscillate. At what point does the system have the least potential energy?

Accepted Answer

A)  at the highest point 
B)  at one-fourth of the distance between the highest point and lowest point 
C)  at the lowest point 
D)  at the point where the spring is unstretched 
E)  at the equilibrium point 
A)  at the highest point 
B)  at one-fourth of the distance between the highest point and lowest point 
C)  at the lowest point 
D)  at the point where the spring is unstretched 
E)  at the equilibrium point

Question 15

A 1200-kg car whose springs have an effective force constant of 2.66 × 106 N/m is moving along the highway with its tires out of balance. The tires have a radius of 40.6 cm. At what speed will the driver experience large vibrations?

Accepted Answer

A)  19.1 m/s 
B)  22.2 m/s 
C)  18.9 m/s 
D)  17.4 m/s 
E)  25.0 m/s 
A)  19.1 m/s 
B)  22.2 m/s 
C)  18.9 m/s 
D)  17.4 m/s 
E)  25.0 m/s

Question 16

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. How long does it take it to travel 11.43 cm?

Accepted Answer

A)  3.53 s 
B)  0.882 s 
C)  1.13 s 
D)  1.76 s 
E)  2.65 s 
A)  3.53 s 
B)  0.882 s 
C)  1.13 s 
D)  1.76 s 
E)  2.65 s

Question 17

A sewing machine needle moves with a frequency of 2.5 Hz. Approximately how long does it take it to move from the highest point to the lowest point in its travel?

Accepted Answer

A)  0.40 s 
B)  0.10 s 
C)  0.20 s 
D)  0.80 s 
E)  1.25 s 
A)  0.40 s 
B)  0.10 s 
C)  0.20 s 
D)  0.80 s 
E)  1.25 s

Question 18

A pendulum makes 12 complete swings in 8.0 s. (a) What is its frequency?
(b) What is its period?

Accepted Answer

The answer of A pendulum makes 12 complete swings in...

Question 19

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26 s2)t]. What is the acceleration of the mass when t = 0.825 s?

Accepted Answer

A)  9.89 cm/s2 
B)  -9.89 cm/s2 
C)  10.6 cm/s2 
D)  -10.6 cm/s2 
E)  0 cm/s2 
A)  9.89 cm/s2 
B)  -9.89 cm/s2 
C)  10.6 cm/s2 
D)  -10.6 cm/s2 
E)  0 cm/s2

Question 20

A mass on a spring undergoes SHM. When the mass is at its maximum displacement from equilibrium, its instantaneous velocity

Accepted Answer

A)  is maximum. 
B)  is less than maximum, but not zero. 
C)  is zero. 
D)  cannot be determined without mass information given. 
E)  cannot be determined without spring constant information given. 
A)  is maximum. 
B)  is less than maximum, but not zero. 
C)  is zero. 
D)  cannot be determined without mass information given. 
E)  cannot be determined without spring constant information given.

Exam 13: Oscillations About Equilibrium

In a grandfather clock, the pendulum measures the time elapsed. A grandfather clock is gaining time. Should you shorten or lengthen the pendulum?

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 its acceleration at t = 2.50 s?

In 1851 Jean Bernard Leon Foucault demonstrated the rotation of the Earth using a pendulum 11.0 m long, which was set up in the Paris Observatory. What was the period of oscillation of the pendulum?

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. In any 4.60 s time interval, how much time is the mass more than 4.15 cm away from x = 0 cm?

A mass of 1.53 kg is attached to a spring and the system is undergoing simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. What is the total mechanical energy of the system?

For a periodic process, the number of cycles per unit time is called the

If your heart is beating at 76.0 beats per minute, what is the frequency of your heart's oscillations?

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 its speed at t = 2.50 s?

The position of an air-track cart that is oscillating on a spring is given by x = (12.4 cm) cos[(6.35 s-1)t]. At what value of t after t = 0 s is the cart first located at x = 8.47 cm?

A mass of 1.53 kg is attached to a spring and the system is undergoing simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm. What is the speed of the mass when it is 3.00 cm from its equilibrium position?

An oscillating system has a small amount of damping. It is observed that in the course of 20.0 s the amplitude has decreased from A to A/2. What additional time is required for the amplitude to decrease to A/4?

FIGURE 13-1 -Curve B in Figure 13-1 represents

A mass m is attached to a vertical spring with a force constant k, it oscillates with a period T. If the spring is cut to one third of its original length and the same mass is attached to it, the new period of oscillation will be

A vertical spring has a mass hanging from it, which is displaced from the equilibrium position and begins to oscillate. At what point does the system have the least potential energy?

A 1200-kg car whose springs have an effective force constant of 2.66 × 106 N/m is moving along the highway with its tires out of balance. The tires have a radius of 40.6 cm. At what speed will the driver experience large vibrations?

A sewing machine needle moves up and down in simple harmonic motion with an amplitude of 1.27 cm and a frequency of 2.55 Hz. How long does it take it to travel 11.43 cm?

A sewing machine needle moves with a frequency of 2.5 Hz. Approximately how long does it take it to move from the highest point to the lowest point in its travel?

A pendulum makes 12 complete swings in 8.0 s. (a) What is its frequency? (b) What is its period?

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26 s2)t]. What is the acceleration of the mass when t = 0.825 s?

A mass on a spring undergoes SHM. When the mass is at its maximum displacement from equilibrium, its instantaneous velocity

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The position of an air-track cart that is oscillating on a spring is given by x = (12.4 cm) cos[(6.35 s^-1)t]. At what value of t after t = 0 s is the cart first located at x = 8.47 cm?

A 1200-kg car whose springs have an effective force constant of 2.66 × 10⁶ N/m is moving along the highway with its tires out of balance. The tires have a radius of 40.6 cm. At what speed will the driver experience large vibrations?

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26 s²)t]. What is the acceleration of the mass when t = 0.825 s?