Question 1

The simple harmonic motion of an object is described by the graph shown in the figure.What is the equation for the position x(t)of the object as a function of time t? 
A)x(t)= (4.0 m)sin[(2π/8.0 s)t + π/3.0]
B)x(t)= (4.0 m)cos[(2π/8.0 s)t + 2π/3.0]
C)x(t)= (4.0 m)cos[(2π/8.0 s)t + π/3.0]
D)x(t)= (4.0 m)cos[(2π/8.0 s)t - π/3.0]
E)x(t)= (8.0 m)cos[(2π/8.0 s)t + π/3.0]

Accepted Answer

D

Question 2

A frictionless pendulum clock on the surface of the earth has a period of 1.00 s.On a distant planet,the length of the pendulum must be shortened slightly to have a period of 1.00 s.What is true about the acceleration due to gravity on the distant planet?
A)The gravitational acceleration on the planet is slightly greater than g.
B)The gravitational acceleration on the planet is slightly less than g.
C)The gravitational acceleration on the planet is equal to g.
D)We cannot tell because we do not know the mass of the pendulum.

Accepted Answer

The period of a pendulum is given by T=2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. Since the period T is fixed and the length L is being shortened, it follows that g must be smaller on the distant planet. Therefore, the gravitational acceleration on the planet is slightly less than g.

Question 3

An object is executing simple harmonic motion.What is true about the acceleration of this object? (There may be more than one correct choice.)
A)The acceleration is a maximum when the displacement of the object is a maximum.
B)The acceleration is a maximum when the speed of the object is a maximum.
C)The acceleration is a maximum when the displacement of the object is zero.
D)The acceleration is zero when the speed of the object is a maximum.
E)The acceleration is a maximum when the object is instantaneously at rest.

Accepted Answer

A,D,E

Question 4

The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm)cos[(1.26s^-1)t].At time t = 0.815 s, (a)how fast is the object moving? (b)what is the magnitude of the acceleration of the object?

Accepted Answer

The answer of The position of an object that is...

Question 5

Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s?
A) 
B) 
C) 
D) 
E)

Accepted Answer

The answer of Which of following graphs describes simple periodic...

Question 6

A mass M is attached to an ideal massless spring.When this system is set in motion with amplitude A,it has a period T.What is the period if the amplitude of the motion is increased to 2A?
A)2T
B)T/2
C)  T
D)4T
E)T

Accepted Answer

The answer of A mass M is attached to an...

Question 7

A frictionless 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 because the period is independent of the amplitude and mass.

Accepted Answer

The answer of A frictionless pendulum released from 65 degrees...

Question 8

In simple harmonic motion,the speed is greatest at that point in the cycle when
A)the magnitude of the acceleration is a maximum.
B)the displacement is a maximum.
C)the magnitude of the acceleration is a minimum.
D)the potential energy is a maximum.
E)the kinetic energy is a minimum.

Accepted Answer

In simple harmonic motion, the speed is greatest at the equilibrium position, where the displacement is zero and the magnitude of the acceleration is a minimum. This is because all the energy is kinetic at this point.

Question 9

If we double only the amplitude of a vibrating ideal mass-and-spring system,the mechanical energy of the system
A)increases by a factor of  .
B)increases by a factor of 2.
C)increases by a factor of 3.
D)increases by a factor of 4.
E)does not change.

Accepted Answer

The mechanical energy of a vibrating ideal mass-and-spring system is proportional to the square of the amplitude of vibration. Therefore, doubling the amplitude will increase the mechanical energy by a factor of 2^2 = 4.

Question 10

A restoring force of magnitude F acts on a system with a displacement of magnitude x.In which of the following cases will the system undergo simple harmonic motion? A)F B)F sin x C)F x² D)F x E)F 1/x

Accepted Answer

The answer of A restoring force of magnitude F acts...

Question 11

A simple harmonic oscillator has an amplitude of 3.50 cm and a maximum speed of 26.0 cm/s.What is its speed when the displacement is 1.75 cm?
A)12.0 cm/s
B)22.5 cm/s
C)14.2 cm/s
D)15.0 cm/s
E)17.0 cm/s

Accepted Answer

The answer of A simple harmonic oscillator has an amplitude...

Question 12

If we double only the spring constant of a vibrating ideal mass-and-spring system,the mechanical energy of the system
A)increases by a factor of  .
B)increases by a factor of 2.
C)increases by a factor of 3.
D)increases by a factor of 4.
E)does not change.

Accepted Answer

The answer of If we double only the spring constant...

Question 13

A mass M is attached to an ideal massless spring.When this system is set in motion,it has a period T.What is the period if the mass is doubled to 2M?
A)2T
B)T/2
C)  T
D)4T
E)T

Accepted Answer

The answer of A mass M is attached to an...

Question 14

The position x of an object varies with time t.For which of the following equations relating x and t is the motion of the object simple harmonic motion? (There may be more than one correct choice.) A)x = 5 sin²3t B)x = 8 cos 3t C)x = 4 tan 2t D)x = 5 sin 3t E)x = 2 cos(3t - 1)

Accepted Answer

The answer of The position x of an object varies...

Question 15

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.
(a)What is the maximum speed of the needle?
(b)What is the maximum acceleration of the needle?

Accepted Answer

The answer of A sewing machine needle moves up and...

Question 16

In designing buildings to be erected in an area prone to earthquakes,what relationship should the designer try to achieve between the natural frequency of the building and the typical earthquake frequencies?
A)The natural frequency of the building should be exactly the same as typical earthquake frequencies.
B)The natural frequency of the building should be very different from typical earthquake frequencies.
C)The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly higher.
D)The natural frequency of the building should be almost the same as typical earthquake frequencies but slightly lower.

Accepted Answer

To minimize the risk of resonance, which can amplify the effects of an earthquake and cause significant damage, the natural frequency of the building should be very different from the typical earthquake frequencies. This helps in reducing the amplitude of vibrations experienced by the building during an earthquake.

Question 17

An object is undergoing simple harmonic motion with frequency f = 9.7 Hz and an amplitude of  .At t = 0.00 s the object is at x = 0.00 m.How long does it take the object to go from  .00 m to

Accepted Answer

The answer of An object is undergoing simple harmonic motion...

Question 18

A certain frictionless simple pendulum having a length L and mass M swings with period T.If both L and M are doubled,what is the new period?
A)4T
B)2T
C)  T
D)T
E)T/4

Accepted Answer

The answer of A certain frictionless simple pendulum having a...

Question 19

An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B.When the kinetic energy of the object is a minimum,the object is located
A)at either A or B.
B)midway between A and B.
C)1/3 of the distance from A to B.
D)1/4 of the distance from A to B.
E)1/  times the distance from A to B.

Accepted Answer

The kinetic energy of the object is at a minimum at the extreme points A and B, where the velocity is zero. At any other point between A and B, the object will have some velocity and therefore some kinetic energy.

Question 20

If we double only the mass of a vibrating ideal mass-and-spring system,the mechanical energy of the system
A)increases by a factor of  .
B)increases by a factor of 2.
C)increases by a factor of 3.
D)increases by a factor of 4.
E)does not change.

Accepted Answer

The answer of If we double only the mass of...

Quiz 15: Oscillations

The simple harmonic motion of an object is described by the graph shown in the figure.What is the equation for the position x(t) of the object as a function of time t?

A frictionless pendulum clock on the surface of the earth has a period of 1.00 s.On a distant planet,the length of the pendulum must be shortened slightly to have a period of 1.00 s.What is true about the acceleration due to gravity on the distant planet?

An object is executing simple harmonic motion.What is true about the acceleration of this object? (There may be more than one correct choice.)

The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm)cos[(1.26s^-1)t].At time t = 0.815 s, (a)how fast is the object moving? (b)what is the magnitude of the acceleration of the object?

Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s?

A mass M is attached to an ideal massless spring.When this system is set in motion with amplitude A,it has a period T.What is the period if the amplitude of the motion is increased to 2A?

A frictionless 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 because the period is independent of the amplitude and mass.

In simple harmonic motion,the speed is greatest at that point in the cycle when

If we double only the amplitude of a vibrating ideal mass-and-spring system,the mechanical energy of the system

A restoring force of magnitude F acts on a system with a displacement of magnitude x.In which of the following cases will the system undergo simple harmonic motion?

A simple harmonic oscillator has an amplitude of 3.50 cm and a maximum speed of 26.0 cm/s.What is its speed when the displacement is 1.75 cm?

If we double only the spring constant of a vibrating ideal mass-and-spring system,the mechanical energy of the system

A mass M is attached to an ideal massless spring.When this system is set in motion,it has a period T.What is the period if the mass is doubled to 2M?

The position x of an object varies with time t.For which of the following equations relating x and t is the motion of the object simple harmonic motion? (There may be more than one correct choice.) A)x = 5 sin²3t B)x = 8 cos 3t C)x = 4 tan 2t D)x = 5 sin 3t E)x = 2 cos(3t - 1)

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. (a)What is the maximum speed of the needle? (b)What is the maximum acceleration of the needle?

In designing buildings to be erected in an area prone to earthquakes,what relationship should the designer try to achieve between the natural frequency of the building and the typical earthquake frequencies?

An object is undergoing simple harmonic motion with frequency f = 9.7 Hz and an amplitude of .At t = 0.00 s the object is at x = 0.00 m.How long does it take the object to go from .00 m to

A certain frictionless simple pendulum having a length L and mass M swings with period T.If both L and M are doubled,what is the new period?

An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B.When the kinetic energy of the object is a minimum,the object is located

If we double only the mass of a vibrating ideal mass-and-spring system,the mechanical energy of the system

Quiz 15: Oscillations

The simple harmonic motion of an object is described by the graph shown in the figure.What is the equation for the position x(t) of the object as a function of time t?

A frictionless pendulum clock on the surface of the earth has a period of 1.00 s.On a distant planet,the length of the pendulum must be shortened slightly to have a period of 1.00 s.What is true about the acceleration due to gravity on the distant planet?

An object is executing simple harmonic motion.What is true about the acceleration of this object? (There may be more than one correct choice.)

The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm)cos[(1.26s-1)t].At time t = 0.815 s, (a)how fast is the object moving? (b)what is the magnitude of the acceleration of the object?

Which of following graphs describes simple periodic motion with amplitude 2.00 cm and angular frequency 2.00 rad/s?

A mass M is attached to an ideal massless spring.When this system is set in motion with amplitude A,it has a period T.What is the period if the amplitude of the motion is increased to 2A?

A frictionless 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 because the period is independent of the amplitude and mass.

In simple harmonic motion,the speed is greatest at that point in the cycle when

If we double only the amplitude of a vibrating ideal mass-and-spring system,the mechanical energy of the system

A restoring force of magnitude F acts on a system with a displacement of magnitude x.In which of the following cases will the system undergo simple harmonic motion?

A simple harmonic oscillator has an amplitude of 3.50 cm and a maximum speed of 26.0 cm/s.What is its speed when the displacement is 1.75 cm?

If we double only the spring constant of a vibrating ideal mass-and-spring system,the mechanical energy of the system

A mass M is attached to an ideal massless spring.When this system is set in motion,it has a period T.What is the period if the mass is doubled to 2M?

The position x of an object varies with time t.For which of the following equations relating x and t is the motion of the object simple harmonic motion? (There may be more than one correct choice.) A)x = 5 sin23t B)x = 8 cos 3t C)x = 4 tan 2t D)x = 5 sin 3t E)x = 2 cos(3t - 1)

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. (a)What is the maximum speed of the needle? (b)What is the maximum acceleration of the needle?

In designing buildings to be erected in an area prone to earthquakes,what relationship should the designer try to achieve between the natural frequency of the building and the typical earthquake frequencies?

An object is undergoing simple harmonic motion with frequency f = 9.7 Hz and an amplitude of .At t = 0.00 s the object is at x = 0.00 m.How long does it take the object to go from .00 m to

A certain frictionless simple pendulum having a length L and mass M swings with period T.If both L and M are doubled,what is the new period?

An object is attached to a vertical ideal massless spring and bobs up and down between the two extreme points A and B.When the kinetic energy of the object is a minimum,the object is located

If we double only the mass of a vibrating ideal mass-and-spring system,the mechanical energy of the system

The position of an object that is oscillating on an ideal spring is given by the equation x = (12.3 cm)cos[(1.26s^-1)t].At time t = 0.815 s, (a)how fast is the object moving? (b)what is the magnitude of the acceleration of the object?

The position x of an object varies with time t.For which of the following equations relating x and t is the motion of the object simple harmonic motion? (There may be more than one correct choice.) A)x = 5 sin²3t B)x = 8 cos 3t C)x = 4 tan 2t D)x = 5 sin 3t E)x = 2 cos(3t - 1)