Question 1

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?

Accepted Answer

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

Question 2

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?

Accepted Answer

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 3

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.

Accepted Answer

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

Question 4

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?

Accepted Answer

A) T  
B) T/  
C) T/6 
D) 6T 
E) T/3

Question 5

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?

Accepted Answer

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 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. )

Accepted Answer

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

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

Accepted Answer

A) 4 
B) 2 
C)   
D) 2/π

Question 8

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?

Accepted Answer

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 9

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.

Accepted Answer

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

Question 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?

Accepted Answer

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

Question 11

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. )

Accepted Answer

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 12

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?

Accepted Answer

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

Question 13

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?

Accepted Answer

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

Question 14

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.

Accepted Answer

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

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 elastic potential energy is a maximum?

Accepted Answer

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

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?

Accepted Answer

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 17

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?

Accepted Answer

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

Question 18

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?

Accepted Answer

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

Question 19

If the amplitude of the motion of a simple harmonic oscillator is doubled,by what factor does the maximum speed of the oscillator change?

Accepted Answer

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

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 fast.Which of the following adjustments of the weight would make it more accurate? (There could be more than one correct choice. )

Accepted Answer

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.

Exam 13: Oscillations About Equilibrium

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?

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?

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 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?

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

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 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.

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?

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 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.

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?

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?

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 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?

If the amplitude of the motion of a simple harmonic oscillator is doubled,by what factor does the maximum speed of the oscillator change?

Exam 13: Oscillations About Equilibrium

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?

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?

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 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?

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

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 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.

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?

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 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.

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?

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?

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 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?

If the amplitude of the motion of a simple harmonic oscillator is doubled,by what factor does the maximum speed of the oscillator change?

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 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 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 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.