Deck 13: Oscillations About Equilibrium

Question 1

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 angular frequency is doubled.
C)The amplitude is doubled.
D)The period is reduced to one-half of what it was.
E)The angular frequency is reduced to one-half of what it was.

Answer 1

The angular frequency is doubled.
The period is reduced to one-half of what it was.

Question 2

An object that hangs from the ceiling of a stationary elevator by an ideal spring oscillates with a period T.If the elevator accelerates upward with acceleration 2g,what will be the period of oscillation of the object?

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

Answer 2

T

Question 3

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

Answer 3

graph a

Question 4

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 5

A mass on a spring undergoes SHM.When the mass is at its maximum distance from the equilibrium position,which of the following statements about it 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.

Question 6

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 elastic 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)at none of the above points

Question 7

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 8

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 9

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 10

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

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

Question 11

A mass on a spring undergoes SHM.When the mass passes through the equilibrium position,which of the following statements about it 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.

Question 12

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 13

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 14

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 15

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

Question 16

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 17

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

Question 18

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 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 its elastic 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)at none of the above points

Question 20

Grandfather clocks are designed so they can be adjusted by moving the weight 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 weight would make it more accurate? (There could be more than one correct choice. )

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

Question 21

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 22

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 23

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 24

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 25

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 26

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 27

An object is undergoing simple harmonic motion of amplitude 2.3 m.If the maximum velocity of the object is 10 m/s,what is the object's angular frequency?

A)4.3 rad/s
B)4.8 rad/s
C)3.5 rad/s
D)4.0 rad/s

Question 28

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 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 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 30

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 31

A simple pendulum and a mass 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 32

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 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 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 34

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 35

Grandfather clocks are designed so they can be adjusted by moving the weight 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 weight would make it more accurate? (There could be more than one correct choice. )

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

Question 36

A simple pendulum that consists of a small ball of mass m and a massless wire of length L swings with a period T.Suppose now that the mass is rearranged so that mass of the ball was reduced but the mass of the wire was increased,with the total mass remaining m and the length being L.What is true about the new period of swing? (There could be more than one correct choice. )

A)The new period is T because the total mass m has not changed.
B)The new period is T because the length L has not changed.
C)The new period is greater than T.
D)The new period is less than T
E)The new period is T because neither L nor m have changed.

Question 37

The position of an object that is oscillating on a spring is given by the equation 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 38

A simple pendulum and a mass 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 39

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 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 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 41

A 0.25 kg harmonic oscillator has a total mechanical energy of 4.1J. If the oscillation amplitude is 20.0 cm. What is the oscillation frequency?

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

Question 42

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 43

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 44

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 45

A 0.39-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant)is 570 N/m.
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 x=0.057 m. 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 46

A 0.150-kg air track cart is attached to an ideal spring with a force constant (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 47

A block attached to an ideal spring of force constant (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 48

A 3.7-kg block on a horizontal frictionless surface is attached to an ideal spring whose force constant (spring constant)is 450 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.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 49

A 92-kg man climbs into 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,which 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 50

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

Question 51

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 (force constant)of the bungee cord?

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

Question 52

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 × 10^-3 Hz
C)0.52 Hz
D)1.6 Hz

Question 53

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 54

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 -0.90m. A velocity of -0.80 m/s And an acceleration of +2.9 m/ s². The force constant (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 55

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 force constant (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 56

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 57

A 2.0-kg block on a frictionless table is connected to two springs whose opposite ends are fixed to walls,as shown in the figure.The springs have force constants (spring constants)k₁ and k₂.What is the oscillation angular frequency of the block if k₁ =7.6 N/ m And k₂=5.0 N/m?

A)2.5 rad/s
B)3.5 rad/s
C)0.40 rad/s
D)0.56 rad/s

Question 58

An object attached to an ideal spring oscillates with an angular frequency of 2.81 rad/s.The object has a maximum displacement at t = 0.00 s of 0.232 m.If the force constant (spring constant)is
What is the potential energy stored in the mass-spring system when t = 1.42 s?

A)0.350 J
B)0.256 J
C)0.329 J
D)0.399 J

Question 59

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 force constant (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 60

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 force constant (spring constant)of the spring is 12 N/m. 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 61

An astronaut has landed on an asteroid and conducts an experiment to determine the acceleration of gravity on that asteroid.He uses a simple 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?

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 62

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 63

The period of a simple pendulum that is 1.00 m long on another planet is
What is the acceleration due to gravity on this planet if the mass of the pendulum bob is 1.5 kg?

A)14.3 m/s²
B)13.3 m/s²
C)15.7 m/s²
D)17.2 m/s²

Question 64

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 65

A 0.50-kg object is attached to an ideal spring of spring constant (force 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 66

A ball vibrates back and forth from the free end of an ideal spring having a force constant (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 67

A Christmas ornament made from a thin hollow glass sphere hangs from a small hook at its surface.It is observed to oscillate with a frequency of 2.50 Hz in a city where g = 9.80 m/s².What is the radius of the ornament? The moment of inertia of a hollow sphere of mass M and radius R about a point on its edge is 5MR²/3.

A)1.84 cm
B)3.68 cm
C)2.38 cm
D)3.98 cm
E)4.69 cm

Question 68

A simple pendulum takes 2.00 s to make one compete swing.If we now triple the length,how long will it take for one complete swing?

A)6.00 s
B)3.46 s
C)2.00 s
D)1.15 s
E)0.667 s

Question 69

An astronaut has landed on Planet N-40 and conducts an experiment to determine the acceleration due to gravity on that planet.She uses a simple pendulum that is 0.640 m long and measures that 10 complete oscillations 26.0 s.What is the acceleration of gravity on Planet N-40?

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 70

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

Question 71

A simple pendulum having a bob of mass M has a period T.If you double M but change nothing else,what would be the new period?

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

Question 72

A thin hoop is supported in a vertical plane by a nail.What should the radius of the hoop be in order for it to have a period of oscillation of 1.00 s? The moment of inertia of a hoop of mass M and radius R about a point on its rim is 2MR².

A)0.0154 m
B)0.0621 m
C)0.124 m
D)0.1876 m
E)0.248 m

Question 73

A 0.150-kg cart that is attached to an ideal spring with a force constant (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 74

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 4.9m.
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 75

A simple pendulum has a period T on Earth.If it were used on Planet X,where the acceleration due to gravity is 3 times what it is on Earth,what would its period be?

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

Question 76

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.How long would it have taken for Foucault's pendulum to make one complete swing back to its starting point if g = 9.81 m/s² at the observatory?

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

Question 77

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.How long would it take for the bob in this pendulum to move from the position of maximum displacement down to the equilibrium point?

A)4.11 s
B)21.5 s
C)2.58 s
D)32.2 s
E)42.9 s

Question 78

If both the mass of a simple pendulum and its length are doubled,the period will

A)be unchanged.
B)increase by a factor of 2.
C)increase by a factor of 4.
D)increase by a factor of .
E)increase by a factor of 1/ .

Question 79

How much mass should be attached to a vertical ideal spring having a spring constant (force 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