Deck 13: Oscillations About Equilibrium

Question 1

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

Answer 1

If all the soldiers march in step,a single frequency disturbance is applied to the bridge.If that frequency coincides with a natural frequency of oscillation of the bridge,a large amplitude response is possible.By breaking step,the driving force will have many random frequencies of smaller amplitude.

Question 2

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.

Answer 2

-(95.0 cm/s)sin[(5.46 s^-1)t]

Question 3

For periodic motion, the maximum displacement from the equilibrium point is called the

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

Answer 3

amplitude.

Question 4

Two players are enjoying a steady volley in a game of ping-pong, in which the motion of the ball is repeated regularly. Is the motion of the ball simple harmonic motion?

Question 5

If the amplitude of the motion of a simple harmonic oscillator is doubled, by what factor does the frequency of the oscillator change?

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

Question 6

If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum speed of the oscillator change?

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

Question 7

Should the tuner on a radio have small or large damping?

Question 8

The time for one cycle of a periodic process is called the

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

Question 9

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

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

Question 10

If the frequency of the motion of a simple harmonic oscillator is doubled, by what factor does the maximum acceleration of the oscillator change?

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

Question 11

A mass is oscillating on a spring with an amplitude of 8.3 cm and a period of 4.6 s. Write an expression for its position, x, as a function of time, if x is equal to 8.3 cm at t = 0 s.

Question 12

In designing buildings to be erected in an area prone to earthquakes, should you try to have a small or a large amount of damping?

Question 13

Which of the following are characteristics of a mass in simple harmonic motion?
I. The motion repeats at regular intervals.
II. The motion is sinusoidal.
III. The restoring force is proportional to the displacement from equilibrium.

A) I and II only
B) I and III only
C) II and III only
D) all of the above
E) none of the above

Question 14

In simple harmonic motion, the acceleration is proportional to

A) the velocity.
B) the frequency.
C) the amplitude.
D) the displacement.
E) all of the above

Question 15

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

Question 16

In designing buildings to be erected in an area prone to earthquakes, what relationship should the designer try to achieve between the natural frequencies of the building and the typical earthquake frequencies?

Question 17

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 acceleration of the particle as a function of time.

Question 18

Increasing the damping constant beyond that required for critical damping makes the system approach equilibrium more quickly.

Question 19

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

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

Question 20

In simple harmonic motion, the speed is greatest at that point in the cycle when

A) the magnitude of the acceleration is a maximum.
B) the displacement is a maximum.
C) the magnitude of the acceleration is a minimum.
D) the potential energy is a maximum.
E) the kinetic energy is a minimum.

Question 21

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) 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 22

Doubling only the mass of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?

A) increases the energy by a factor of square root of two
B) increases the energy by a factor of two
C) increases the energy by a factor of three
D) increases the energy by a factor of four
E) produces no change

Question 23

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

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.

Question 24

Doubling only the amplitude of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?

A) increases the energy by a factor of square root of two
B) increases the energy by a factor of two
C) increases the energy by a factor of three
D) increases the energy by a factor of four
E) produces no change

Question 25

Grandfather clocks are designed in a way that the weight at the bottom of the pendulum can be moved up or down by turning a small screw. Suppose you have a grandfather clock at home that runs slow. Should you turn the adjusting screw so as to raise the weight or lower the weight?

A) Raise it.
B) Lower it.
C) It doesn't matter if you raise or lower the weight as long as you displace it by the right amount.
D) It doesn't matter if you raise or lower the weight, as long as you displace it with the correct initial velocity.
E) Raising or lowering the weight doesn't help. The screw is there so that you can add or take away weight.

Question 26

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) 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 27

The total mechanical energy of a simple harmonic oscillator is

A) zero as it passes the equilibrium point.
B) zero when it reaches the maximum displacement.
C) a maximum when it passes through the equilibrium point.
D) a minimum when it passes through the equilibrium point.
E) constant.

Question 28

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?

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

Question 29

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a maximum?

A) at either A or B
B) midway between A and B
C) one-third of the way between A and B
D) one-fourth of the way between A and B
E) none of the above

Question 30

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its potential energy is a minimum?

A) at either A or B
B) midway between A and B
C) one-third of the way between A and B
D) one-fourth of the way between A and B
E) none of the above

Question 31

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

A) is a 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.

Question 32

Both pendulum A and B are 3.0 m long. The period of A is T. Pendulum A is twice as heavy as pendulum B. What is the period of B?

A) 0.71T
B) T
C) 1.4T
D) 2T
E) 3T

Question 33

A mass on a spring undergoes SHM. When the mass passes through the equilibrium position, its instantaneous velocity

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.

Question 34

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

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 35

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its potential energy is a maximum?

A) at either A or B
B) midway between A and B
C) one-third of the way between A and B
D) one-fourth of the way between A and B
E) none of the above

Question 36

A mass is attached to a vertical spring and bobs up and down between points A and B. Where is the mass located when its kinetic energy is a minimum?

A) at either A or B
B) midway between A and B
C) one-third of the way between A and B
D) one-fourth of the way between A and B
E) none of the above

Question 37

On the Moon, the acceleration of gravity is g/6. If a pendulum has a period T on Earth, what will its period be on the Moon?

A) T
B) T/
C) T/6
D) 6T
E) T/3

Question 38

If you take a given pendulum to the Moon, where the acceleration of gravity is less than on Earth, the resonant frequency of the pendulum will

A) increase.
B) decrease.
C) not change.
D) become zero.
E) either increase or decrease; it depends on its length to mass ratio.

Question 39

Doubling only the spring constant of a vibrating mass-and-spring system produces what effect on the system's mechanical energy?

A) increases the energy by a factor of square root of two
B) increases the energy by a factor of two
C) increases the energy by a factor of three
D) increases he energy by a factor of four
E) produces no change

Question 40

A mass oscillates on the end of a spring, both on Earth and on the Moon. Where is the period the greatest?

A) Earth
B) the Moon
C) the same on both Earth and the Moon
D) Cannot be determined from the information given.

Question 41

A tuning fork is set into vibration with a frequency of 512 Hz. How many oscillations does it undergo in 1 minute?

A) 30700
B) 8.53
C) 26.8
D) 1610
E) 512

Question 42

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?

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 43

A 0.50-kg mass is attached to a spring of spring constant 20 N/m along a horizontal, frictionless surface. The object oscillates in simple harmonic motion and has a speed of 1.5 m/s at the equilibrium position. (a) What is the amplitude of vibration?
(b) At what location are the kinetic energy and the potential energy the same?

Question 44

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

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

Question 45

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?

Question 46

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

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

Question 47

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/10?

Question 48

A 1.5-kg mass attached to spring with a force constant of 20.0 N/m oscillates on a horizontal, frictionless track. At t= 0, the mass is released from rest at x= 10.0 cm. (That is, the spring is stretched by 10.00 cm.) (a) Determine the frequency of the oscillations.
(b) Determine the maximum speed of the mass. Where does the maximum speed occur?
(c) Determine the maximum acceleration of the mass. Where does the maximum acceleration occur?
(d) Determine the total energy of the oscillating system.
(e) Express the displacement as a function of time.

Question 49

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

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

Question 50

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

Question 51

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 period of this motion?

A) 1.74 s
B) 1.15 s
C) 1.32 s
D) 0.869 s
E) 0.314 s

Question 52

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 upward with constant acceleration?

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

Question 53

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

Question 54

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. If the walking speed of the adult is 1.3 m/s, what is the walking speed of the child?

Question 55

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?

Question 56

The position of a mass that is oscillating on a spring is given by x = (18.3 cm) cos[(2.35 s^-1)t]. What is the frequency of this motion?

A) 0.426 Hz
B) 1.34 Hz
C) 2.67 Hz
D) 0.128 Hz
E) 0.374 Hz

Question 57

A simple pendulum consists of a mass M attached to a weightless string of length L. For this system, when undergoing small oscillations

A) the frequency is proportional to the amplitude.
B) the frequency is inversely proportional to the amplitude.
C) the period is proportional to the amplitude.
D) the frequency is independent of the mass M.
E) the frequency is independent of the length L.

Question 58

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. (a) What is the maximum speed of the needle?
(b) What is the maximum acceleration of the needle?

Question 59

The quartz crystal in a digital watch has a frequency of 32.8 kHz. What is its period of oscillation?

A) 3.05 × 10^-5 s
B) 1.53 × 10^-5 s
C) 9.58 × 10^-5 s
D) 1.91 × 10^-4 s
E) 9.71 × 10^-6 s

Question 60

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

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

Question 61

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?

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 62

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

Question 63

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

Question 64

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. What is the maximum acceleration of the needle?

A) 8.26 cm/s²
B) 16.5 cm/s²
C) 18.1 cm/s²
D) 326 cm/s²
E) 163 cm/s²

Question 65

A 92-kg man climbs onto a car with worn out shock absorbers and this causes the car to drop down 4.5 cm. As he drives along, he hits a bump, and this starts the car oscillating at an angular frequency of 4.52 rad/s. What is the mass of the car?

A) 890 kg
B) 760 kg
C) 920 kg
D) 990 kg
E) 1900 kg

Question 66

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

Question 67

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?

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 68

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?

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

Question 69

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

Question 70

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

Question 71

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?

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

Question 72

An air-track cart is attached to a spring and completes one oscillation every 5.67 s. At t = 0 s the cart is released at a distance of 0.250 m from its equilibrium position. What is the position of the cart when t = 29.6 s?

A) x = 0.0460 m
B) x = 0.210 m
C) x = 0.218 m
D) x = 0.342 m
E) x = -0.218 m

Question 73

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?

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 74

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26 s^-1)t]. What is the speed of the mass when t = 0.805 s?

A) - 13.2 cm/s
B) 13.2 cm/s
C) 8.19 cm/s
D) - 8.19 cm/s
E) 0 cm/s

Question 75

A mass of 0.250 kg is attached to a spring and undergoes simple harmonic oscillations with a period of 0.640 s. What is the force constant of the spring?

A) 2.45 N/m
B) 12.1 N/m
C) 24.1 N/m
D) 0.102 N/m
E) 0.610 N/m

Question 76

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?

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

Question 77

An 85.0-kg man climbs onto a 900-kg car with worn out shock absorbers and whose springs have an effective force constant of 125 kN/m. As he drives along, he hits a bump, and this starts the car oscillating with simple harmonic motion. What is the smallest amplitude of the oscillations that will cause him to bounce from his seat?

A) 7.06 cm
B) 7.73 cm
C) 7.88 cm
D) 8.95 cm
E) 8.42 cm

Question 78

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

Question 79

A simple harmonic oscillator has an amplitude of 3.50 cm and a maximum speed of 26.0 cm/s. What is its speed when the displacement is 1.75 cm?

A) 12.0 cm/s
B) 22.5 cm/s
C) 14.2 cm/s
D) 15.0 cm/s
E) 17.0 cm/s

Question 80

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. What is the maximum speed of the needle?

A) 3.18 cm/s
B) 4.51 cm/s
C) 20.3 cm/s
D) 10.1 cm/s
E) 6.36 cm/s