Deck 14: Oscillations

Question 1

The period of a simple pendulum in a grandfather clock on another planet is 1.66 s.What is the acceleration due to gravity on this planet? Assume that the length of the pendulum is 1.00 m.

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

Answer 1

14.3 m/s²

Question 2

A mass on a spring has an angular oscillation frequency of 2.81 rad/s.The mass has a maximum displacement (when t = 0 s)of 0.232 m.If the spring constant is 29.8 N/m,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

Answer 2

0.350 J

Question 3

A rotating merry-go-round has an angular velocity of 0.184 rad/s.Find the period of rotation of the merry-go-round.

A)34.1 s
B)5.43 s
C)13.6 s
D)3.91 s

Answer 3

34.1 s

Question 4

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

A)4.4 rad/s
B)4.8 rad/s
C)3.5 rad/s
D)4.0 rad/s

Question 5

A 5.7 kg block attached to a spring executes simple harmonic motion on a frictionless horizontal surface.At time t = 0 s,the block has a displacement of -0.70 m,a velocity of -0.80 m/s,and an acceleration of +2.7 m/s².The amplitude of the motion is closest to:

A)0.81 m
B)2.7 m
C)1.0 m
D)1.1 m
E)1.2 m

Question 6

A child on a swing set swings back and forth.If the length of the supporting cables for the swing is 4.9 m,what is the period of oscillation?

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

Question 7

An object undergoing simple harmonic motion has a maximum displacement of 6.2 m at t = 0.0 s.If the angular frequency of oscillation is 1.6 rad/s,what is the object's displacement when t = 3.5 s?

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

Question 8

The wheels on a particular moving car rotate 486 times per minute.Find the rotational period of the tires.

A)0.123 s
B)0.002 s
C)0.148 s
D)0.172 s

Question 9

A 0.25 kg harmonic oscillator has a total oscillation energy of 4.0 J.If the oscillation amplitude is 20.0 cm,what is the oscillation frequency?

A)4.5 Hz
B)1.4 Hz
C)2.3 Hz
D)3.1 Hz

Question 10

A 0.39 kg block on a horizontal frictionless surface is attached to a spring whose force constant is 570 N/m.The block is pulled from its equilibrium position at x = 0 m to a displacement x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the x-axis (horizontal).When the displacement is x = 0.057 the kinetic energy of the block is closest to:

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

Question 11

A 3.7 kg block on a horizontal frictionless surface is attached to a spring whose force constant is 450 N/m.The block is pulled from its equilibrium position at x = 0 m to a displacement x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the x-axis (horizontal).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 12

A leaky faucet drips 40 times in 30.0 s.What is the frequency of the dripping?

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

Question 13

A mass m = 8.0 kg is attached to a spring and allowed to hang in the Earth's gravitational field.The spring stretches 3.6 cm before it reaches its equilibrium position.If allowed to oscillate,what would be its frequency?

A)2.6 Hz
B)0.45 × 10^-3 Hz
C)0.67 Hz
D)2.1 Hz

Question 14

A 4.8 kg block attached to a spring 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 force 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 15

A 0.16 kg block on a horizontal frictionless surface is attached to a spring whose force constant is 360 N/m.The block is pulled from its equilibrium position at x = 0 m to a displacement x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the x-axis (horizontal).When the displacement is x = -0.037 m,the acceleration of the block is closest to:

A)85 m/s²
B)43 m/s²
C)64 m/s²
D)270 m/s²
E)370 m/s²

Question 16

A 2.0 kg block on a frictionless table is connected to two springs with spring constants k₁ and k2₁ whose opposite ends are fixed to walls,as show in the figure.What is the oscillation angular frequency 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 17

A 56.0 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)17.6 N/m
B)21.1 N/m
C)28.2 N/m

Question 18

A 3.42 kg mass hanging vertically from a spring on the Earth (where g = 9.8 m/s²)undergoes simple oscillatory motion.If the spring constant is 12 N/m,find the period of oscillation of this setup on the moon,where g = 1.6 m/s².

A)3.35 s
B)2.51 s
C)4.35 s
D)5.70 s

Question 19

A 2.0 kg block on a horizontal frictionless surface is attached to a spring whose force constant is 590 N/m.The block is pulled from its equilibrium position at x = 0 m to a displacement x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the x-axis (horizontal).The velocity of the block at time t = 0.10 s is closest to:

A)-1 m/s
B)1 m/s
C)0.2 m/s
D)-0.2 m/s
E)zero

Question 20

A 0.12 kg block on a horizontal frictionless surface is attached to a spring whose force constant is 570 N/m.The block is pulled from its equilibrium position at x = 0 m to a displacement x = +0.080 m and is released from rest.The block then executes simple harmonic motion along the x-axis (horizontal).The displacement of the block at time t = 0.20 s is closest to:

A)0.01 m
B)-0.01 m
C)0.08 m
D)-0.08 m
E)0.1 m

Question 21

An object (object A) of mass M is attached to a spring with spring constant k. The other end of the spring is attached to a rigid wall. A second object (object B) of mass M is attached to two springs (one on each side of the object), each with a spring constant of k/2 (the other ends of the springs are attached to rigid walls). Each object is displaced and let go, causing harmonic motion. How does the frequency of oscillation of object A compare to that of object B?

A)The frequencies are the same.
B)The frequency of object B is higher than that of A.
C)The frequency of object B is lower than that of A.

Question 22

A pendulum released from 65 degrees with the vertical will vibrate with the same frequency as if it were released from 5 degrees with the vertical.

Question 23

Simple harmonic motion occurs only if the restoring force is directly proportional to the first power of the displacement.

Question 24

The length of a pendulum changes by thermal expansion.If the length increases by 0.1%,what would be the change in the period?

A)increase by
B)increase by 0.1%
C)decrease by 0.1%
D)decrease by 0.99

Question 25

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 1.4
E)increase by a factor of 0.71.

Question 26

A disk and a ball both of radius r and mass m,are suspended at a point on the edge of the object at the maximum radius.Which has the smaller period of oscillation?

A)ball
B)disk
C)the same
D)Not enough information

Question 27

For an object undergoing simple harmonic motion,

A)the acceleration is greatest when the speed is greatest.
B)the displacement is greatest when the speed is greatest.
C)the acceleration is greatest when the displacement is greatest.
D)the maximum potential energy is larger than the maximum kinetic energy.
E)the total energy oscillates at frequency f = .

Question 28

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

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

Question 29

A mass is oscillating at the end of a spring.Neither the period of oscillation nor the maximum speed of the mass depend on the amplitude of the motion.

Question 30

If the frequency of a harmonic oscillator doubles,by what factor does the maximum value of acceleration change?

A)4
B)2
C)
D)2/π

Question 31

Two identical objects,each with a mass M,are attached to each other via a spring with a spring constant k.The two objects are oscillating such that one is always moving in the opposite direction and with the same speed as the other.If the spring were replaced with a stiffer spring having a spring constant equal to 2k,and the objects were replaced with objects having a mass of 2M,the period of oscillation would

A)remain the same.
B)increase.
C)decrease.

Question 32

Two identical objects,each with a mass M,are attached to each other via a spring with a spring constant k.The two objects are oscillating such that one is always moving in the opposite direction and with the same speed as the other.If the two objects were made to oscillate with a higher amplitude,

A)the average kinetic energy of each object would increase.
B)the average potential energy of the spring would increase.
C)the total mechanical energy would increase.
D)All of the above

Question 33

A mass attached to a very light spring executes simple harmonic motion.If you want to double its total energy,you should

A)double the amplitude of vibration while changing nothing else.
B)double the force constant of the spring while changing nothing else.
C)double both the amplitude and force constant.
D)double the mass while changing nothing else.
E)double both the mass and amplitude of vibration.

Question 34

As a pendulum swings through its cycle,the mass is moving fastest and has its greatest acceleration at the bottom of the swing.

Question 35

A mass oscillates at the end of a spring.If you double both the mass and the spring constant,the period of oscillation is unchanged.

Question 36

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,its period would be:

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

Question 37

A mass attached to a spring would vibrate with the same frequency in an orbiting satellite as it does at Earth's surface,but a pendulum would not have the same frequency that it has at Earth's surface.

Question 38

If you double the mass of a pendulum,the period of vibration does not change.

Question 39

If pendulum A is twice as long as pendulum B,the period of oscillation of A will be twice as long as the period of B,even if they have different masses.

Question 40

Two identical objects,each with a mass M,are attached to each other via a spring with a spring constant k.The two objects are oscillating such that one is always moving in the opposite direction and with the same speed as the other.If the two objects were made to oscillate with a higher amplitude,the period of oscillation would

A)remain the same.
B)increase.
C)decrease.

Question 41

If the total energy of a harmonic oscillator is reduced by 1/3,what is the change in the amplitude of the oscillations?

A)
B)
C)1/3
D)3