Deck 14: Oscillations

Question 1

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.

Answer 1

the magnitude of the acceleration is a minimum.

Question 2

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

Answer 2

all of the above

Question 3

A student designs a clock using a mass and a spring. Each oscillation of the mass advances the clock by one second. When the student builds the clock, he discovers he erred and each oscillation takes two seconds. What change can he make to fix the clock?

A)double the amplitude of the oscillations
B)quadruple the spring constant of the spring
C)double the spring constant of the spring
D)quadruple the mass
E)double the mass

Answer 3

quadruple the spring constant of the spring

Question 4

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 5

A mass M is attached to a spring with spring constant k. When this system is set in motion with amplitude A, it has a period T. What is the period if the mass is doubled to 2M?

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

Question 6

Simple harmonic motion is always sinusoidal.

Question 7

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 8

The period and frequency of a simple pendulum depend on the mass of the pendulum bob.

Question 9

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 10

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

Question 11

Any oscillating system for which the net restoring force is directly proportional to the displacement is said to exhibit simple harmonic motion.

Question 12

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

Question 13

The projection of circular motion onto a straight line is simple harmonic motion.

Question 14

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 15

A mass M is attached to a spring with spring constant k. When this system is set in motion with amplitude A, it has a period T. What is the period if the amplitude of the motion is increased to 2A?

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

Question 16

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

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

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

Question 19

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

Question 20

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 21

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 22

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 23

A nail is stuck into the side of a car tire. As the car drives down a level road at constant speed, which of the following is simple harmonic motion?

A)the motion of the center of the tire
B)the vertical component of motion of the nail
C)the horizontal component of motion of the nail
D)both answers A and B
E)none of the above

Question 24

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 25

What is impossible about the following situation? An object in simple harmonic motion has an equilibrium position x = 0.00 m. At some instant in time, the position of the object is +3.00 m, the velocity is -2.00 m/s, and the acceleration is +9.00 m/s².

A)The numerical value of the velocity is smaller than the distance from the equilibrium position, but the numerical value of the magnitude of the acceleration is larger than the distance from equilibrium.
B)The velocity is opposite in direction to the displacement.
C)The acceleration is greater than the speed.
D)The speed is less than the displacement.
E)The displacement from equilibrium and the acceleration are in the same direction.

Question 26

The x-component of motion of an object is given by x(t) = A_xcos(ω_xt + φ_x) and the y-component of motion of the object is given by y(t) = A_ycos(ω_yt + φ_y). What relationships between the A,ω, and φ parameters must be true so that the motion of the object is on a circle?

A)A_x = A_y, ω_x = ω_y, and φ_x = φ_y
B)A_x = ±A_y, ω_x = ±ω_y
C)A_x = ±A_y, ω_x = ω_y, and φ_x = φ_y ± π/2
D)A_x = A_y, ω_x = ±ω_y, and φ_x = φ_y
E)A_x = ±A_y, ω_x = ±ω_y, and φ_x = φ_y ± π/2

Question 27

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 28

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 29

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 30

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 31

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 32

FIGURE 14-1
Which of following is a graph of simple periodic motion with amplitude 2.00 cm, angular frequency 2.00 s^-1?

A)

B)

C)

D)

E)

Question 33

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 34

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 35

FIGURE 14-1
The simple harmonic motion of an object is shown in Fig. 14-1. What is the position of the object as a function of time?

A)x(t) = (4.0 m)sin[(2π/8.0 s)t + π/3.0]
B)x(t) = (4.0 m)cos[(2π/8.0 s)t + 2π/3.0]
C)x(t) = (4.0 m)cos[(2π/8.0 s)t + π/3.0]
D)x(t) = (4.0 m)cos[(2π/8.0 s)t - π/3.0]
E)x(t) = (8.0 m)cos[(2π/8.0 s)t + π/3.0]

Question 36

A pendulum clock on the surface of the earth has a period of 1.00 s. On a distant planet, the length of the pendulum must be shortened slightly to have a period of 1.00 s. What is true about the acceleration of gravity on the distant planet?

A)The gravitational acceleration of the planet is 0.
B)The gravitational acceleration of the planet is slightly greater than g.
C)The gravitational acceleration of the planet is slightly less than g.
D)There is no gravitational acceleration on the planet.
E)The gravitational acceleration of the planet is equal to g.

Question 37

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 38

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 39

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 40

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 41

FIGURE 14-2
Curve C in Fig. 14-2 represents

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

Question 42

FIGURE 14-2
Curve B in Fig. 14-2 represents

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

Question 43

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 44

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 45

FIGURE 14-2
Curve A in Fig. 14-2 represents

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

Question 46

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.
(a) What is the value of t the first time after t = 0 s that that the mass is at x = 4.15 cm?
(b) What is its acceleration at t = 2.50 s?

Question 47

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 fast. 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 48

For a forced vibration, the amplitude of vibration is found to depend on the

A)sum of the external frequency and the natural frequency.
B)difference of the external frequency and the natural frequency.
C)product of the external frequency and the natural frequency.
D)ratio of the external frequency and the natural frequency.
E)ratio of the natural frequency and the external frequency.

Question 49

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 50

A pendulum is made by suspending a solid circular disk from a pivot point that is at the edge of the disk with the plane of the disk lying in the vertical plane. The period of oscillation of the disk is T. If a disk with the same radius but a mass four times is great is suspended the same way, what will be its period of oscillation?

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

Question 51

For a damped driven harmonic oscillator, the frequency at which the amplitude is maximum is

A)greater than the natural frequency of oscillation.
B)equal to the natural frequency of oscillation.
C)at an infinite frequency.
D)zero.
E)less than the natural frequency of oscillation.

Question 52

When a mass of 180 g is attached to a vertical spring and lowered to its equilibrium position, it is found that the spring extends 12 cm. If the mass is now displaced from its equilibrium position, what is the period of the resulting oscillations?

A)2.2 s
B)3.7 s
C)0.69 s
D)9.0 s
E)1.5 s

Question 53

Increasing the amplitude of a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no other changes in the system.)

A)The frequency increases.
B)The frequency decreases.
C)There is no change in the frequency.
D)The frequency depends on the displacement, not the amplitude.

Question 54

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 55

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 56

The design considerations for a timing mechanism require that a mass of 1.6 g should undergo 5 oscillations per second when it is attached to a spring. What should the force constant of a spring be to achieve this?

A)15.6 N/m
B)3.1 N/m
C)7.2 N/m
D)1.6 N/m
E)8.0 N/m

Question 57

The amplitude of a 3.00-kg object in simple harmonic motion is 10.0 m. The maximum speed of the object is 5.00 m/s What is the frequency of simple harmonic motion?

A)0.500 Hz
B)2.78 × 10^-2 Hz
C)2.00 Hz
D)7.96 × 10^-2 Hz
E)3.14 Hz

Question 58

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 59

Increasing the spring constant k of a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no change in the system's mass m.)

A)The frequency increases.
B)The frequency decreases.
C)There is no change in the frequency.
D)The frequency increases if the ratio k/m is greater than or equal to 1.
E)The frequency decreases if the ratio k/m is less than 1.

Question 60

Increasing the mass m of a mass-and-spring system causes what kind of change in the resonant frequency of the system? (Assume no change in the system's spring constant k.)

A)The frequency increases.
B)The frequency decreases.
C)There is no change in the frequency.
D)The frequency increases if the ratio k/m is greater than or equal to 1.
E)The frequency decreases if the ratio k/m is less than 1.

Question 61

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26s^-1)t]. What is the velocity of the mass when t = 0.815 s?

A)- 13.3 cm/s
B)13.3 cm/s
C)8.02 cm/s
D)- 8.02 cm/s
E)0 cm/s

Question 62

The tip of the needle of a sewing machine executes simple harmonic motion with an amplitude of 1.2 cm and an angular frequency ω = 62 rad/s. What is the total distance traveled by the needle in 1.9 s?

A)27 cm
B)40 cm
C)1.1 cm
D)90 cm
E)140 cm

Question 63

The maximum displacement of a mass attached to a spring is 0.122 m, while its highest acceleration is 0.953 m/s². What is its maximum speed?

A)0.358 m/s
B)0.108 m/s
C)0.831 m/s
D)0.341 m/s
E)0.538 m/s

Question 64

What is the total energy of a 300-g mass that is attached to a horizontal spring with a force constant of 260 N/m and oscillates along a frictionless horizontal surface with an amplitude of 8.0 cm?

A)21 J
B)0.83 J
C)2.4 J
D)1.6 J
E)6.2 J

Question 65

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?

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 66

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 with an amplitude of 7.50 cm. What is the total mechanical energy of the system?

A)0.0201 J
B)0.0101 J
C)0.269 J
D)0.134 J
E)0 J

Question 67

The position of a mass that is oscillating on a spring is given by x = (12.3 cm) cos[(1.26s^-1)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 68

An air conditioning unit is vibrating in simple harmonic motion with a period of 0.27 s and a range (from the maximum in one direction to the maximum in the other) of 3.0 cm. At t = 0 it is at its central position and moving in the +x direction. What is its position when t = 55 s?

A)x = -0.430 cm
B)x = -0.511 cm
C)x = 0.511 cm
D)x = -1.41 cm
E)x = -1.44 cm

Question 69

A simple harmonic oscillator has an amplitude of 3.50 cm and a maximum speed of 28.0 cm/s. What is its speed when the displacement is 1.75 cm?

A)12.0 cm/s
B)24.2 cm/s
C)14.2 cm/s
D)15.0 cm/s
E)17.0 cm/s

Question 70

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?

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

Question 71

The amplitude of a 3.00-kg object in simple harmonic motion is 6.00 m. The maximum acceleration of the object is 5.00 m/s². What is the period of simple harmonic motion?

A)6.88 s
B)1.20 s
C)0.278 s
D)0.833 s
E)7.54 s

Question 72

The position of an air-track cart that is oscillating on a spring is given by x = (12.4 cm) cos[(6.35s^-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 73

The position of a mass that is oscillating on a spring is given by x = (17.4 cm) cos[(5.46s^-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 74

The velocity of a mass attached to a spring is given by v = (1.5 cm/s) sin(ωt + π/2), where ω = 3.0 rad/s. What is the corresponding expression for x?

A)x = -(4.50 cm) sin(ωt + π/2)
B)x = (4.50 cm) cos(ωt + π/2)
C)x = -(0.50 cm) cos(ωt - π/2)
D)x = -(0.50 cm) cos(ωt + π/2)
E)x = -(0.50 cm) sin(ωt + π/2)

Question 75

A 30-g bullet traveling horizontally at 300 m/s strikes a 1.0-kg block which is attached to a horizontal spring with a force constant of 2000 N/m and rests on a frictionless horizontal surface. The spring is on the far side of the block and aligned with the direction of travel of the bullet. The bullet becomes embedded in the block and, as a result of the impact, and the block slides against the spring. How far is the spring compressed before it reverses its direction of travel?

A)0.20 m
B)0.58 m
C)1.2 m
D)0.40 m
E)0.039 m

Question 76

What is the maximum kinetic energy of a 2.00-kg mass moving with simple harmonic motion with an amplitude 5.00 cm and period 0.300 s?

A)1.10 J
B)0.444 J
C)0.222 J
D)0.174 J
E)0.0278 J

Question 77

The position of a mass that is oscillating on a spring is given by x = (18.3 cm) cos[(2.35s^-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 78

A 4.20-g bullet embeds itself in a 20.0-kg block, which is attached to a horizontal spring with a force constant of 980 N/m. The maximum compression of the spring is 2.40 cm. What is the speed of the bullet just before it hits the block?

A)800 m/s
B)700 m/s
C)672 m/s
D)900 m/s
E)952 m/s

Question 79

The maximum speed of a 3.00-kg object in simple harmonic motion is 4.00 m/s. The maximum acceleration of the object is 5.00 m/s². What is the period of simple harmonic motion?

A)1.25 s
B)0.417 s
C)0.800 s
D)5.03 s
E)3.75 s

Question 80

A 16.2-g bullet with an initial speed of 850 m/s embeds itself in a 40.0-kg block, which is attached to a horizontal spring with a force constant of 1000 N/m. What is the maximum compression of the spring?

A)6.34 cm
B)5.57 cm
C)3.42 cm
D)1.26 cm
E)6.88 cm