Deck 20: Vibrational Motion

Question 1

A object on a spring undergoes SHM.When the object passes through the equilibrium position,which of the following statements about object-spring system are true? (There could be more than one correct choice.)

A)Its acceleration is zero.
B)Its speed is zero.
C)Its elastic potential energy is zero.
D)Its kinetic energy is a maximum.
E)Its total mechanical energy is zero.

Answer 1

A,C,D

Question 2

The figure shows a graph of the velocity v as a function of time t for a system undergoing simple harmonic motion.Which one of the following graphs represents the acceleration of this system as a function of time?

A)graph a
B)graph b
C)graph c
D)graph d

Answer 2

B

Question 3

Grandfather clocks are designed so they can be adjusted by moving the bob at the bottom of the pendulum up or down.Suppose you have a grandfather clock at home that runs slow.Which of the following adjustments of the bob would make it more accurate? (There could be more than one correct choice.)

A)Raise the bob.
B)Lower the bob.
C)Add more mass to the bob.
D)Remove some mass from the bob.
E)Increase the amplitude of swing by a small amount.

Answer 3

A

Question 4

The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion.Which one of the following graphs represents the acceleration of this system as a function of time?

A)graph a
B)graph b
C)graph c
D)graph d

Question 5

The figure shows a graph of the position x as a function of time t for a system undergoing simple harmonic motion.Which one of the following graphs represents the velocity of this system as a function of time?

A)graph a
B)graph b
C)graph c
D)graph d

Question 6

Identical balls oscillate with the same period T on Earth.Ball A is attached to an ideal spring and ball B swings back and forth to form a simple pendulum.These systems are now taken to the Moon,where g = 1.6 m/s²,and set into oscillation.Which of the following statements about these systems are true? (There could be more than one correct choice.)

A)Both systems will have the same period on the Moon as on Earth.
B)On the Moon, ball A will take longer to complete one cycle than ball B.
C)On the Moon, ball B will take longer to complete one cycle than ball A.
D)On the Moon, ball A will execute more vibrations each minute than ball B.
E)On the Moon, ball B will execute more vibrations each minute than ball A.

Question 7

In simple harmonic motion,when is the speed the greatest? (There could be more than one correct choice.)

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

Question 8

If we double the frequency of a system undergoing simple harmonic motion,which of the following statements about that system are true? (There could be more than one correct choice.)

A)The period is doubled.
B)The amplitude is doubled.
C)The period is reduced to one-half of what it was.

Question 9

An object attached to an ideal spring executes simple harmonic motion.If you want to double the total energy of the object-spring system,you could

A)double the amplitude of vibration.
B)double the spring constant of the spring.
C)double both the amplitude and spring constant.
D)double the mass of the object.
E)double both the mass of the object and amplitude of vibration.

Question 10

Two simple pendulums,A and B,are each 3.0 m long,and the period of pendulum A is T.Pendulum A is twice as heavy as pendulum B.What is the period of pendulum B?

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

Question 11

An object is attached to a vertical spring and bobs up and down between points A and B.Where is the object located when the elastic potential energy of the system object-spring 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)at none of the above points

Question 12

A simple harmonic oscillator oscillates with frequency f when its amplitude is A.If the amplitude is now doubled to 2A,what is the new frequency?

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

Question 13

Grandfather clocks are designed so they can be adjusted by moving the bob at the bottom of the pendulum up or down.Suppose you have a grandfather clock at home that runs fast.Which of the following adjustments of the bob would make it more accurate? (There could be more than one correct choice.)

A)Raise the bob.
B)Lower the bob.
C)Add more mass to the bob.
D)Remove some mass from the bob.
E)Decrease the amplitude of swing by a small amount.

Question 14

The total mechanical energy of a simple harmonic oscillating system 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)a non-zero constant.

Question 15

An object is attached to a vertical spring and bobs up and down between points A and B.Where is the object 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)at none of the above points

Question 16

In simple harmonic motion,when is the magnitude of the acceleration the greatest? (There could be more than one correct choice.)

A)when the speed is a maximum
B)when the displacement is a zero
C)when the magnitude of the displacement is a maximum
D)when the potential energy is a maximum
E)when the kinetic energy is a minimum

Question 17

An object is attached to a vertical spring and bobs up and down between points A and B.Where is the object 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)at none of the above points

Question 18

An object attached to a spring undergoes SHM.When the object is at its maximum distance from the equilibrium position,which of the following statements are true? (There could be more than one correct choice.)

A)The object's acceleration is zero.
B)The object's speed is zero.
C)The elastic potential energy of the system object-spring is zero.
D)The kinetic energy of the system object-spring is a maximum.
E)The total mechanical energy of the system object-spring is zero.

Question 19

An object is attached to a vertical spring and bobs up and down between points A and B.Where is the object located when the elastic potential energy of the system object-spring 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)at none of the above points

Question 20

A ball swinging at the end of a massless string,as shown in the figure,undergoes simple harmonic motion.At what point (or points)is the magnitude of the instantaneous acceleration of the ball the greatest?

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

Question 21

An air-track cart is attached to a spring and completes one oscillation every 5.67 s in simple harmonic motion.At time t = 0.00 s the cart is released at the position x = +0.250 m.What is the position of the cart when t = 29.6 s?

A)x = 0.0461 m
B)x = 0.210 m
C)x = 0.218 m
D)x = 0.342 m
E)x = -0.218 m

Question 22

The position of an air-track cart that is oscillating on a spring is given by the equation x = (12.4 cm)cos[(6.35 s^-1)t].At what value of t after t = 0.00 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 23

A point on the string of a violin moves up and down in simple harmonic motion with an amplitude of 1.24 mm and a frequency of 875 Hz.
(a)What is the maximum speed of that point in SI units?
(b)What is the maximum acceleration of the point in SI units?

Question 24

A sewing machine needle moves in simple harmonic motion with a frequency of 2.5 Hz and an amplitude of 1.27 cm.
(a)How long does it take the tip of the needle to move from the highest point to the lowest point in its travel?
(b)How long does it take the needle tip to travel a total distance of 11.43 cm?

Question 25

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

A)30.5 µs
B)15.3 µs
C)95.8 µs
D)0.191 ms
E)9.71 µs

Question 26

A simple pendulum and an object oscillating on an ideal spring both have period T in an elevator at rest.If the elevator now accelerates downward uniformly at 2 m/s²,what is true about the periods of these two systems?

A)Both periods would remain the same.
B)Both periods would increase.
C)Both periods would decrease.
D)The period of the pendulum would increase but the period of the spring would stay the same.
E)The period of the pendulum would decrease but the period of the spring would stay the same.

Question 27

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 are the (a)maximum speed and (b)maximum acceleration of the tip of the needle?

Question 28

If a pendulum makes 12 complete swings in 8.0 s,what are its (a)frequency and (b)period?

Question 29

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 would the period of the pendulum change if the supporting chain were to break,putting the elevator into freefall?

A)The period does not change.
B)The period increases slightly.
C)The period decreases slightly.
D)The period becomes zero.
E)The period becomes infinite because the pendulum would not swing.

Question 30

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

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

Question 31

A simple pendulum and an object oscillating on an ideal spring both have period T in an elevator at rest.If the elevator now moves downward at a uniform 2 m/s,what is true about the periods of these two systems?

A)Both periods would remain the same.
B)Both periods would increase.
C)Both periods would decrease.
D)The period of the pendulum would increase but the period of the spring would stay the same.
E)The period of the pendulum would decrease but the period of the spring would stay the same.

Question 32

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 increases if the upward acceleration is more than g/2 but decreases if the upward acceleration is less than g/2.

Question 33

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 velocity?

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 34

If a floating log is seen to bob up and down 15 times in 1.0 min as waves pass by you,what are the frequency and period of the oscillation?

Question 35

A guitar string is set into vibration with a frequency of 512 Hz.How many oscillations does it undergo each minute?

A)30,700
B)8.53
C)26.8
D)1610
E)512

Question 36

A leaky faucet drips 40 times in What is the frequency of the dripping?

A)1.3 Hz
B)0.75 Hz
C)1.6 Hz
D)0.63 Hz

Question 37

The position of a cart that is oscillating on a spring is given by the equation x = (12.3 cm)cos[(1.26 s^-1)t].When t = 0.805 s,what are the (a)velocity and (b)acceleration of the cart?

Question 38

If the frequency of a system undergoing simple harmonic motion doubles,by what factor does the maximum value of acceleration change?

A)4
B)2
C)
D)2/π

Question 39

The position of an object that is oscillating on a spring is given by the equation x = (18.3 cm)cos[(2.35 s^-1)t].What are the (a)frequency,(b)amplitude,and (c)period of this motion?

Question 40

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 41

A 0.150-kg air track cart is attached to an ideal spring with a spring 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 42

In a supermarket,you place a 22.3-N (around 5 lb)bag of oranges on a scale,and the scale starts to oscillate at 2.7 Hz.What is the spring constant of the spring of the scale?

A)650 N/m
B)600 N/m
C)330 N/m
D)820 N/m
E)410 N/m

Question 43

When a laboratory sample of unknown mass is placed on a vertical spring-scale having a spring constant of 467 N/m,the system obeys the equation y = (4.4 cm)cos(33.3 s^-1 t).What is the mass of this laboratory sample?

Question 44

A package is oscillating on a spring scale with a period of 4.60 s.At time t = 0.00 s the package has zero speed and is at x = 8.30 cm.At what time after t = 0.00 s will the package first be 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 45

A 4.8-kg block attached to an ideal spring executes simple harmonic motion on a frictionless horizontal surface.At time t = 0.00 s,the block has a displacement of a velocity of and an acceleration of The spring constant of the spring is closest to

A)15 N/m.
B)14 N/m.
C)13 N/m.
D)12 N/m.
E)11 N/m.

Question 46

An object undergoing simple harmonic motion has a maximum displacement of at If the angular frequency of oscillation is what is the object's displacement when

A)4.8 m
B)5.6 m
C)3.7 m
D)3.1 m

Question 47

When a 0.350-kg package is attached to a vertical spring and lowered slowly,the spring stretches 12.0 cm.The package is now displaced from its equilibrium position and undergoes simple harmonic oscillations when released.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 48

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

Question 49

If the amplitude 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)It does not change.
D)1/2
E)1/4

Question 50

An object oscillates such that its position x as a function of time t obeys the equation x = (0.222 m)sin(314 s^-1 t),where t is in seconds.
(a)In one period,what total distance does the object move?
(b)What is the frequency of the motion?
(c)What is the position of the object when t = 1.00 s?

Question 51

The equation of motion of a particle undergoing simple harmonic motion in the y direction is y = (2.0 cm)sin(0.60 s^-1 t).At time t = 0.60 s determine the particle's (a)position,(b)velocity,and (c)acceleration.

Question 52

A ball is oscillating on an ideal 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 t,if x is equal to 8.3 cm at t = 0.0 s.Use the cosine function.

Question 53

A 0.25 kg harmonic oscillator has a total mechanical energy of If the oscillation amplitude is what is the oscillation frequency?

A)4.6 Hz
B)1.4 Hz
C)2.3 Hz
D)3.2 Hz

Question 54

A 0.250-kg stone is attached to an ideal spring and undergoes simple harmonic oscillations with a period of 0.640 s.What is the spring 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 55

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

Question 56

A 1.15-kg beaker (including its contents)is placed on a vertical spring scale.When the system is sent into vertical vibrations,it obeys the equation y = (2.3 cm)cos(17.4 s^-1 t).What is the spring constant of the spring scale,assuming it to be ideal?

Question 57

An object is oscillating on a spring with a period of 4.60 s.At time t = 0.00 s the object has zero speed and is at x = 8.30 cm.What is the acceleration of the object 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)0.00 cm/s²

Question 58

A 51.8-kg bungee jumper jumps off a bridge and undergoes simple harmonic motion.If the period of oscillation is 11.2 s,what is the spring constant of the bungee cord?

A)16.3 N/m
B)19.6 N/m
C)26.1 N/m

Question 59

A 3.42-kg stone hanging vertically from an ideal spring on the earth undergoes simple harmonic motion at a place where g = 9.80 m/s².If the spring constant of the spring is find the period of oscillation of this setup on a planet where g = 1.60 m/s².

A)3.35 s
B)2.51 s
C)4.36 s
D)5.70 s

Question 60

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)It does not change.
D)1/2
E)1/4

Question 61

How much mass should be attached to a vertical ideal spring having a spring constant of 39.5 N/m so that it will oscillate at 1.00 Hz?

A)39.5 kg
B)2.00 kg
C)1.00 kg
D)1.56 kg
E)6.29 kg

Question 62

A 1.5-kg cart attached to an ideal spring with a spring constant of 20 N/m oscillates on a horizontal,frictionless track.At time t = 0.00 s,the cart is released from rest at position x = 10 cm from the equilibrium position.
(a)What is the frequency of the oscillations of the cart?
(b)Determine the maximum speed of the cart.Where does the maximum speed occur?
(c)Find the maximum acceleration of the mass.Where does the maximum acceleration occur?
(d)How much total energy does this oscillating system contain?
(e)Express the displacement as a function of time using a cosine function.

Question 63

An object of mass m = 8.0 kg is attached to an ideal spring and allowed to hang in the earth's gravitational field.The spring stretches before it reaches its equilibrium position.If it were now allowed to oscillate by this spring,what would be its frequency?

A)3.4 Hz
B)0.28 x 10^-3 Hz
C)0.52 Hz
D)1.6 Hz

Question 64

An object of mass 6.8 kg is attached to an ideal spring of force constant (spring constant)1720 N/m.The object is set into simple harmonic motion,with an initial velocity of and an initial displacement of Calculate the maximum speed the object reaches during its motion.

Question 65

A 0.150-kg cart that is attached to an ideal spring with a spring constant of 3.58 N/m 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 66

A block attached to an ideal spring of spring constant 15 N/m executes simple harmonic motion on a frictionless horizontal surface.At time t = 0 s,the block has a displacement of -0.90 m, a velocity of -0.80 m/s, and an acceleration of +2.9 m/s² .The mass of the block is closest to

A)2.3 kg
B)2.6 kg
C)4.7 kg
D)9.4 kg

Question 67

A 0.16-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant)is 360 N/m.The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the horizontal x-axis.When the position is x = -0.037 m,what is the acceleration of the block?

A)83 m/s²
B)43 m/s²
C)64 m/s²
D)270 m/s²
E)370 m/s²

Question 68

A 0.50-kg object is attached to an ideal 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.At what distance from the equilibrium position are the kinetic energy and potential energy of the system the same?

A)0.017 m
B)0.029 m
C)0.12 m
D)0.17 m

Question 69

A geologist suspends a 0.30-kg stone on an ideal spring.In equilibrium the stone stretches the spring 2.0 cm downward.The stone is then pulled an additional distance of 1.0 cm down and released from rest.
(a)Write down the equation for the vertical position y of the stone as a function of time t,using the cosine function.Take the origin at the equilibrium point of the stone,with the positive y direction upward.
(b)How fast is the stone moving at a time equal to 1/3 of its period of motion?

Question 70

A 0.50-kg object is attached to an ideal 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.What are (a)the total energy and (b)the amplitude of vibration of the system?

Question 71

A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant)is The block is pulled from its equilibrium position at x = 0.000 m to a displacement x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the horizontal x-axis.When the position of the block is its kinetic energy is closest to

A)0.90 J.
B)0.84 J.
C)0.95 J.
D)1.0 J.
E)1.1 J.

Question 72

What is the length of a simple pendulum with a period of 2.0 s?

A)20 m
B)0.99 m
C)1.2 m
D)1.6 m
E)0.87 m

Question 73

A 2.0 kg box is traveling at 5.0 m/s on a smooth horizontal surface when it collides with and sticks to a stationary 6.0 kg box.The larger box is attached to an ideal spring of force constant (spring constant)150 N/m,as shown in the figure.Find (a)the amplitude of the resulting oscillations of this system,(b)the frequency of the oscillations and (c)the period of the oscillations.

Question 74

A 0.50-kg box is attached to an ideal spring of spring constant 20 N/m on a horizontal,frictionless floor.The box 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 distance from the equilibrium position are the kinetic energy and the potential energy the same?

Question 75

A 0.30-kg block of wood is suspended on a spring.In equilibrium the wood stretches the spring 2.0 cm downward.The wood is then pulled an additional distance of 1.0 cm down and released from rest.
(a)How long does it take the wood to make 3 complete cycles of vibration?
(b)How much total mechanical energy does this system contain if we choose the total potential energy (elastic and gravitational)to be zero at the equilibrium position of the hanging block?

Question 76

A 34-kg child on an 18-kg swing set swings back and forth through small angles.If the length of the very light supporting cables for the swing is how long does it take for each complete back-and-forth swing? Assume that the child and swing set are very small compared to the length of the cables.

A)4.4 s
B)4.8 s
C)5.3 s
D)5.7 s

Question 77

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

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

Question 78

A ball vibrates back and forth from the free end of an ideal spring having a spring constant of 20 N/m.If the amplitude of this motion is 0.30 m,what is the kinetic energy of the ball when it is 0.30 m from its equilibrium position?

A)0.00 J
B)0.22 J
C)0.45 J
D)0.90 J
E)1.4 J

Question 79

A 3.7-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant)is The block is pulled from its equilibrium position at x = 0.000 m to a position x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the horizontal x-axis.The maximum elastic potential energy of the system is closest to

A)1.4 J.
B)1.3 J.
C)1.6 J.
D)1.7 J.
E)1.8 J.

Question 80

A 1.53-kg piece of iron is hung by a vertical ideal spring.When perturbed slightly,the system is moves up and down in simple harmonic oscillations with a frequency of 1.95 Hz and an amplitude of 7.50 cm.If we choose the total potential energy (elastic and gravitational)to be zero at the equilibrium position of the hanging iron,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)0.000 J