# Quiz 14: Oscillations

Physics & Astronomy

Q 1Q 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.

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Multiple Choice

B, D

Q 2Q 2

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

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Multiple Choice

C

Q 3Q 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 velocity of this system as a function of time?
A)graph a
B)graph b
C)graph c
D)graph d

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Multiple Choice

B

Q 4Q 4

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

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Multiple Choice

Q 5Q 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 acceleration of this system as a function of time?
A)graph a
B)graph b
C)graph c
D)graph d

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Multiple Choice

Q 6Q 6

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

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Multiple Choice

Q 7Q 7

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

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Multiple Choice

Q 8Q 8

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.

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Multiple Choice

Q 9Q 9

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.

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Multiple Choice

Q 10Q 10

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

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Multiple Choice

Q 11Q 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.

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Multiple Choice

Q 12Q 12

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.

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Multiple Choice

Q 13Q 13

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

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Multiple Choice

Q 14Q 14

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

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Multiple Choice

Q 15Q 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 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

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Multiple Choice

Q 16Q 16

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

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Multiple Choice

Q 17Q 17

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

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Multiple Choice

Q 18Q 18

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

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Multiple Choice

Q 19Q 19

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/s

^{2}, 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.Free

Multiple Choice

Q 20Q 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.

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Multiple Choice

Q 21Q 21

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.

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Multiple Choice

Q 22Q 22

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.

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Multiple Choice

Q 23Q 23

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.

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Multiple Choice

Q 24Q 24

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.

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Multiple Choice

Q 25Q 25

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.

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Multiple Choice

Q 26Q 26

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/s

^{2}, 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.Free

Multiple Choice

Q 27Q 27

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.

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Multiple Choice

Q 28Q 28

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.

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Multiple Choice

Q 29Q 29

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

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Multiple Choice

Q 30Q 30

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

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Multiple Choice

Q 31Q 31

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 wave?

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Essay

Q 32Q 32

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

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Multiple Choice

Q 33Q 33

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

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Multiple Choice

Q 34Q 34

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

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Multiple Choice

Q 35Q 35

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?

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Essay

Q 36Q 36

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?

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Q 37Q 37

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

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Multiple Choice

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Essay

Q 39Q 39

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?

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Essay

Q 40Q 40

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?Free

Essay

Q 41Q 41

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?Free

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Q 42Q 42

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 sFree

Multiple Choice

Q 43Q 43

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

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Multiple Choice

Q 44Q 44

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/sFree

Multiple Choice

Q 45Q 45

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/s

^{2}B)0.784 cm/s^{2}C)11.5 cm/s^{2}D)14.9 cm/s^{2}E)0.00 cm/s^{2}Free

Multiple Choice

Q 46Q 46

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

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Multiple Choice

Q 47Q 47

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.

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Q 48Q 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 velocity of the particle as a function of time using the sine function.Free

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Q 49Q 49

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 particle as a function of time using the cosine function.Free

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Q 50Q 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?Free

Essay

Q 51Q 51

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

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Multiple Choice

Q 52Q 52

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

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Multiple Choice

Q 53Q 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

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Multiple Choice

Q 54Q 54

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

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Multiple Choice

Q 55Q 55

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.Free

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Q 56Q 56

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

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Multiple Choice

Q 57Q 57

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

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Multiple Choice

Q 58Q 58

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

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Multiple Choice

Q 59Q 59

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

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Multiple Choice

Q 60Q 60

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

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Multiple Choice

Q 61Q 61

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 force constant (spring constant)of the spring scale, assuming it to be ideal?Free

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Q 62Q 62

When a laboratory sample of unknown mass is placed on a vertical spring-scale having a force constant (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?Free

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Q 63Q 63

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/s

^{2}. If the force constant (spring constant)of the spring is find the period of oscillation of this setup on a planet where g = 1.60 m/s^{2}. A)3.35 s B)2.51 s C)4.36 s D)5.70 sFree

Multiple Choice

Q 64Q 64

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

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Multiple Choice

Q 65Q 65

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 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.

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Multiple Choice

Q 66Q 66

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 HzFree

Multiple Choice

Q 67Q 67

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)k

_{1}and k_{2}. What is the oscillation angular frequency of the block if and A)2.5 rad/s B)3.5 rad/s C)0.40 rad/s D)0.56 rad/sFree

Multiple Choice

Q 68Q 68

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

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Multiple Choice

Q 69Q 69

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

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Multiple Choice

Q 70Q 70

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/s

^{2}. The mass of the block is closest to A)2.3 kg B)2.6 kg C)4.7 kg D)9.4 kgFree

Multiple Choice

Q 71Q 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.

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Multiple Choice

Q 72Q 72

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/s

^{2}B)43 m/s^{2}C)64 m/s^{2}D)270 m/s^{2}E)370 m/s^{2}Free

Multiple Choice

Q 73Q 73

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.

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Multiple Choice

Q 74Q 74

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 raches during its motion.

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Q 75Q 75

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.

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Q 76Q 76

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/

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Multiple Choice

Q 77Q 77

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?

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Essay

Q 78Q 78

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

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Multiple Choice

Q 79Q 79

A 0.50-kg box is attached to an ideal spring of force constant (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?

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Q 80Q 80

A 1.5-kg cart attached to an ideal spring with a force constant (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.

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Q 81Q 81

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

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Multiple Choice

Q 82Q 82

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. What are (a)the total energy and (b)the amplitude of vibration of the system?

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Essay

Q 83Q 83

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

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Multiple Choice

Q 84Q 84

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

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Multiple Choice

Q 85Q 85

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?

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Q 86Q 86

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

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Multiple Choice

Q 87Q 87

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

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Multiple Choice

Q 88Q 88

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

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Multiple Choice

Q 89Q 89

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/s

^{2}B)13.3 m/s^{2}C)15.7 m/s^{2}D)17.2 m/s^{2}Free

Multiple Choice

Q 90Q 90

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

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Multiple Choice

Q 91Q 91

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

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Multiple Choice

Q 92Q 92

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

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Multiple Choice

Q 93Q 93

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/ .

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Multiple Choice

Q 94Q 94

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

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Multiple Choice

Q 95Q 95

Tarzan swings back and forth on a long vine. His friend Jane notices in amazement that he makes 30 complete swings in 2.4 minutes.
(a)What is the frequency (in hertz)of Tarzan's swing?
(b)How long is the vine he is using?

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Essay

Q 96Q 96

As shown in the figure, a 0.23-kg ball is suspended from a string 6.87 m long and is pulled slightly to the left. As the ball swings through the lowest part of its motion it encounters a spring attached to the wall. The spring pushes against the ball and eventually the ball is returned to its original starting position. Find the time for one complete cycle of this motion if the spring constant (force constant)is (Assume that once the pendulum ball hits the spring there is no effect due to the vertical movement of the ball.)

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Essay

Q 97Q 97

When a certain simple pendulum is set swinging, its angular displacement θ as a function of time t obeys the equation θ = 8.5° cos(2.4 s

^{-1}^{t}). How long is the pendulum?Free

Essay

Q 98Q 98

A spaceship captain lands on an unknown planet. Before venturing forth, he needs to find out the acceleration due to gravity on that planet. All he has available to him is some thin light string, a stopwatch, and a small 2.75-kg metal ball (it was a rough landing). So he lets the ball swing from a 1.5-m length of the string, starting at rest, and measures that it takes 1.9 s for it to swing from the place where he released it to the place where it first stops as it reverses direction. What is the acceleration due to gravity on this planet?

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Essay

Q 99Q 99

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/s

^{2}B)1.66 m/s^{2}C)3.74 m/s^{2}D)2.39 m/s^{2}E)9.81 m/s^{2}Free

Multiple Choice

Q 100Q 100

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/s

^{2}B)1.66 m/s^{2}C)1.74 m/s^{2}D)5.51 m/s^{2}E)0.0544 m/s^{2}Free

Multiple Choice

Q 101Q 101

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/s

^{2}at the observatory? A)6.65 s B)5.63 s C)1.79 s D)2.12 s E)2.58 sFree

Multiple Choice

Q 102Q 102

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

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Multiple Choice

Q 103Q 103

Suppose you want to set up a simple pendulum with a period of 2.50 s. How long should it be
(a)on Earth, at a location where g = 9.80 m/s

^{2}? (b)on a planet where g is 5.00 times what it is on Earth?Free

Essay

Q 104Q 104

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 2MR

^{2}. A)0.0154 m B)0.0621 m C)0.124 m D)0.1876 m E)0.248 mFree

Multiple Choice

Q 105Q 105

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/s

^{2}. 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 5MR^{2}/3. A)1.84 cm B)3.68 cm C)2.38 cm D)3.98 cm E)4.69 cmFree

Multiple Choice