Question 1

Simple harmonic motion: An object is undergoing simple harmonic motion with frequency f = 9.7 Hz and an amplitude of 0.12 m. 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

0.0068 seconds

Question 2

Simple pendulum: 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

False

Question 3

Simple harmonic motion: 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

(a) 20.3 cm/s (b) 326 cm/s²

Question 4

Simple harmonic motion: 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 Simple harmonic motion: The position of an...

Question 5

Simple harmonic motion: 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

The acceleration in simple harmonic motion is proportional to the displacement and is maximum when the displacement is maximum. It is zero when the speed is maximum, and maximum when the object is at rest (at the turning points).

Question 6

Energy in SHM: 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 (SHM), the speed is greatest at the equilibrium position, where the displacement is zero and thus the potential energy is at its minimum. At this point, the magnitude of the acceleration is also at its minimum because acceleration in SHM is proportional to displacement (a = -ω²x). The kinetic energy is at its maximum at this point, not the minimum, making the other options incorrect.

Question 7

Energy in SHM: 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 mechanical energy of a vibrating ideal mass-and-spring system only depends on the amplitude of the vibration and the spring constant, but not on the mass. Doubling the mass will not change the mechanical energy, so the answer is E.

Question 8

Simple pendulum: 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 Simple pendulum: A certain frictionless simple pendulum...

Question 9

Simple harmonic motion: 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 Simple harmonic motion: A restoring force of...

Question 10

Energy in SHM: 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 mass-and-spring system is proportional to the square of the amplitude (E = 1/2 kA^2). If we double the amplitude, the mechanical energy increases by a factor of (2)^2 = 4. Therefore, the correct answer is D.

Question 11

Mass on a spring: 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 Mass on a spring: A mass M...

Question 12

Simple pendulum: 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 simple pendulum is given by T=2π√(L/g), where L is the length of the pendulum and g is the acceleration due to gravity. If the period is the same but the length of the pendulum is shorter, then g must be smaller. Therefore, the gravitational acceleration on the distant planet is slightly less than g.

Question 13

Energy in SHM: 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 Energy in SHM: If we double only...

Question 14

Energy in SHM: 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

At the extreme points A and B, the kinetic energy is zero and the potential energy is maximum. At the equilibrium point, the potential energy is minimum and the kinetic energy is maximum. Therefore, at the point where the kinetic energy is a minimum, the object must be at either point A or B.

Question 15

Mass on a spring: 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 Mass on a spring: A mass M...

Question 16

Resonance: 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 avoid 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 reduces the risk of the building entering into resonance with the earthquake's vibrations.

Question 17

Simple harmonic motion: 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 equation for the displacement of an object undergoing simple harmonic motion is given by
x = A sin(ωt), where A is the amplitude and ω is the angular frequency.
From the given graphs, we can see that graph B represents a sin wave with amplitude of 2.00 cm and angular frequency of 2.00 rad/s, which matches the equation for simple harmonic motion. Therefore, option B is the best choice.

Question 18

Simple harmonic motion: 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 cm)sin[(2π/8.0 s)t + π/3.0]
B) x(t) = (4.0 cm)cos[(2π/8.0 s)t + 2π/3.0]
C) x(t) = (4.0 cm)cos[(2π/8.0 s)t + π/3.0]
D) x(t) = (4.0 cm)cos[(2π/8.0 s)t - π/3.0]
E) x(t) = (8.0 cm)cos[(2π/8.0 s)t + π/3.0]

Accepted Answer

The answer of Simple harmonic motion: The simple harmonic motion...

Question 19

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?
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 Simple harmonic motion: A simple harmonic oscillator...

Question 20

Simple harmonic motion: 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 Simple harmonic motion: The position x of...

Quiz 11: Equilibrium and Elasticity

Simple harmonic motion: An object is undergoing simple harmonic motion with frequency f = 9.7 Hz and an amplitude of 0.12 m. 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

Simple pendulum: 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.

Simple harmonic motion: 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?

Simple harmonic motion: 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?

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

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

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

Simple pendulum: 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?

Simple harmonic motion: 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?

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

Mass on a spring: 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?

Simple pendulum: 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?

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

Energy in SHM: 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

Mass on a spring: 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?

Resonance: 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?

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

Simple harmonic motion: 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?

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?

Simple harmonic motion: 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.)

Simple harmonic motion: 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?