Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

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?

Accepted Answer

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

Question 4

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?

Accepted Answer

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. 
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 5

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. )

Accepted Answer

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. 
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

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?

Accepted Answer

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. 
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 7

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. )

Accepted Answer

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. 
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 8

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.

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

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

Accepted Answer

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 
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 11

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?

Accepted Answer

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

Question 12

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. )

Accepted Answer

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. 
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.

Question 13

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?

Accepted Answer

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

Question 14

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?

Accepted Answer

A) 0.695 s 
B) 0.483 s 
C) 0.286 s 
D) 0.0769 s 
E) 1.44 s 
A) 0.695 s 
B) 0.483 s 
C) 0.286 s 
D) 0.0769 s 
E) 1.44 s

Question 15

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?

Accepted Answer

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

Question 16

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

Accepted Answer

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

Question 17

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?

Accepted Answer

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

Question 18

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?

Accepted Answer

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

Question 19

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?

Accepted Answer

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

Exam 13: Oscillations About Equilibrium

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

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 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 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 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 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 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

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

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?

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 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?

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?

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?

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

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?

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?

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?

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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 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