Question 1

A particle is in simple harmonic motion with period T.At time t = 0 it is at the equilibrium point.At the times listed below it is at various points in its cycle.Which of them is farthest away from the equilibrium point?

Accepted Answer

B

Question 2

An object is undergoing simple harmonic motion.Throughout a complete cycle it:

Accepted Answer

In simple harmonic motion, the acceleration varies because it is directly proportional to the displacement from the equilibrium position and acts in the opposite direction.

Question 3

An object attached to one end of a spring makes 20 vibrations in 10 seconds.Its frequency is:

Accepted Answer

Frequency is the number of vibrations (or cycles) per second.

Frequency = Number of Vibrations / Time

In this case, the number of vibrations is given as 20, and the time is given as 10 seconds.

Frequency = 20/10 = 2 Hz

Therefore, the correct answer is (A) 2 Hz.

Question 4

It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different:

Accepted Answer

The period of an oscillator depends only on the mass and spring constant, and not on the amplitude or kinetic energy. Therefore, if two particles have different periods, they cannot remain in phase with each other over time.

Question 5

Two identical undamped oscillators have the same amplitude of oscillation only if:

Accepted Answer

The answer of Two identical undamped oscillators have the same...

Question 6

An object attached to one end of a spring makes 20 vibrations in 10 seconds.Its angular frequency is:

Accepted Answer

The angular frequency (ω) is calculated using the formula ω = 2πf, where f is the frequency. The frequency is the number of vibrations per second, which is 20/10 = 2 Hz. Therefore, ω = 2π(2) = 4π ≈ 12.6 rad/s.

Question 7

The amplitude of any oscillator will be doubled by:

Accepted Answer

The amplitude of an oscillator is determined by both the initial displacement and the initial speed. Doubling both of these values will lead to a doubling of the amplitude.

Question 8

A particle moves back and forth along the x axis from x = -x_m to x = +x_m, in simple harmonic motion with period T.At time t = 0 it is at x = +x_m.When t = 0.75T:

Accepted Answer

The answer of A particle moves back and forth along...

Question 9

A particle is in simple harmonic motion with period T.At time t=0 it is halfway between the equilibrium point and an end point of its motion, travelling toward the end point.The next time it is at the same place is:

Accepted Answer

In simple harmonic motion, the particle returns to the same position after one complete cycle. Since it starts halfway to the endpoint and moves towards it, it will return to the same position after completing one-third of the cycle, which is T/3.

Question 10

When a body executes simple harmonic motion, its acceleration at the ends of its path must be:

Accepted Answer

The answer of When a body executes simple harmonic motion,...

Question 11

An object attached to one end of a spring makes 20 complete vibrations in 10s.Its period is:

Accepted Answer

The answer of An object attached to one end of...

Question 12

The amplitude and phase constant of an oscillator are determined by:

Accepted Answer

Both the initial displacement and velocity determine the amplitude and phase constant of an oscillator according to the equations:

A = sqrt(x_0^2 + (v_0/ω)^2)   (amplitude)
ϕ = arctan(-v_0/(ωx_0))      (phase constant)

where x_0 is the initial displacement, v_0 is the initial velocity, and ω is the angular frequency. It's important to note that frequency and angular frequency are related but not the same thing, and do not determine the amplitude and phase constant on their own.

Question 13

Frequency f and angular frequency    are related by

Accepted Answer

The relationship between frequency (f) and angular frequency (ω) is given by $f = \frac{\omega}{2\pi}$. This formula is represented by choice D, where $\omega$ is the angular frequency and $2\pi$ is the factor that converts angular frequency to regular frequency.

Question 14

This plot shows a mass oscillating as x = x_m cos (ωt + φ).What are x_m and φ?

Accepted Answer

The answer of This plot shows a mass oscillating as...

Question 15

A particle oscillating in simple harmonic motion is:

Accepted Answer

In simple harmonic motion, the particle reaches its maximum displacement at the ends of its path, where its velocity is zero. However, it is not in equilibrium at these points because there is a net force acting on it. The particle is actually in equilibrium at the center of its path, where the acceleration is zero.

Question 16

A weight suspended from an ideal spring oscillates up and down with a period T.If the amplitude of the oscillation is doubled, the period will be:

Accepted Answer

The period of a mass-spring system is independent of the amplitude of oscillation. It depends on the mass and the spring constant.

Question 17

An oscillatory motion must be simple harmonic if:

Accepted Answer

A simple harmonic motion is characterized by an acceleration that varies sinusoidally with time. Therefore, option D is the best choice. The other options are not sufficient conditions for a motion to be simple harmonic.

Question 18

A block attached to a spring oscillates in simple harmonic motion along the x axis.The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s.Its amplitude and frequency are:

Accepted Answer

The answer of A block attached to a spring oscillates...

Question 19

A particle moves in simple harmonic motion according to x = 2cos(50t), where x is in meters and t is in seconds.Its maximum velocity is:

Accepted Answer

The maximum velocity in simple harmonic motion is given by the amplitude multiplied by the angular frequency. Here, the amplitude is 2 meters, and the angular frequency (from the cosine function's coefficient) is 50 s^-1. Thus, the maximum velocity is 2 * 50 = 100 m/s.

Question 20

In simple harmonic motion, the displacement is maximum when the:

Accepted Answer

In simple harmonic motion, displacement is maximum when the velocity is zero at the extreme points of the motion. This is because at these points, the direction of motion changes and the velocity becomes zero. The acceleration is maximum at these points but the displacement is not maximum at points of maximum acceleration. Therefore, option C is the best choice.

Quiz 15: Oscillations

A particle is in simple harmonic motion with period T.At time t = 0 it is at the equilibrium point.At the times listed below it is at various points in its cycle.Which of them is farthest away from the equilibrium point?

An object is undergoing simple harmonic motion.Throughout a complete cycle it:

An object attached to one end of a spring makes 20 vibrations in 10 seconds.Its frequency is:

It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different:

Two identical undamped oscillators have the same amplitude of oscillation only if:

An object attached to one end of a spring makes 20 vibrations in 10 seconds.Its angular frequency is:

The amplitude of any oscillator will be doubled by:

A particle moves back and forth along the x axis from x = -x_m to x = +x_m, in simple harmonic motion with period T.At time t = 0 it is at x = +x_m.When t = 0.75T:

A particle is in simple harmonic motion with period T.At time t=0 it is halfway between the equilibrium point and an end point of its motion, travelling toward the end point.The next time it is at the same place is:

When a body executes simple harmonic motion, its acceleration at the ends of its path must be:

An object attached to one end of a spring makes 20 complete vibrations in 10s.Its period is:

The amplitude and phase constant of an oscillator are determined by:

Frequency f and angular frequency are related by

This plot shows a mass oscillating as x = x_m cos (ωt + φ) .What are x_m and φ?

A particle oscillating in simple harmonic motion is:

A weight suspended from an ideal spring oscillates up and down with a period T.If the amplitude of the oscillation is doubled, the period will be:

An oscillatory motion must be simple harmonic if:

A block attached to a spring oscillates in simple harmonic motion along the x axis.The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s.Its amplitude and frequency are:

A particle moves in simple harmonic motion according to x = 2cos(50t) , where x is in meters and t is in seconds.Its maximum velocity is:

In simple harmonic motion, the displacement is maximum when the:

Quiz 15: Oscillations

A particle is in simple harmonic motion with period T.At time t = 0 it is at the equilibrium point.At the times listed below it is at various points in its cycle.Which of them is farthest away from the equilibrium point?

An object is undergoing simple harmonic motion.Throughout a complete cycle it:

An object attached to one end of a spring makes 20 vibrations in 10 seconds.Its frequency is:

It is impossible for two particles, each executing simple harmonic motion, to remain in phase with each other if they have different:

Two identical undamped oscillators have the same amplitude of oscillation only if:

An object attached to one end of a spring makes 20 vibrations in 10 seconds.Its angular frequency is:

The amplitude of any oscillator will be doubled by:

A particle moves back and forth along the x axis from x = -xm to x = +xm, in simple harmonic motion with period T.At time t = 0 it is at x = +xm.When t = 0.75T:

A particle is in simple harmonic motion with period T.At time t=0 it is halfway between the equilibrium point and an end point of its motion, travelling toward the end point.The next time it is at the same place is:

When a body executes simple harmonic motion, its acceleration at the ends of its path must be:

An object attached to one end of a spring makes 20 complete vibrations in 10s.Its period is:

The amplitude and phase constant of an oscillator are determined by:

Frequency f and angular frequency are related by

This plot shows a mass oscillating as x = xm cos (ωt + φ) .What are xm and φ?

A particle oscillating in simple harmonic motion is:

A weight suspended from an ideal spring oscillates up and down with a period T.If the amplitude of the oscillation is doubled, the period will be:

An oscillatory motion must be simple harmonic if:

A block attached to a spring oscillates in simple harmonic motion along the x axis.The limits of its motion are x = 10 cm and x = 50 cm and it goes from one of these extremes to the other in 0.25 s.Its amplitude and frequency are:

A particle moves in simple harmonic motion according to x = 2cos(50t) , where x is in meters and t is in seconds.Its maximum velocity is:

In simple harmonic motion, the displacement is maximum when the:

A particle moves back and forth along the x axis from x = -x_m to x = +x_m, in simple harmonic motion with period T.At time t = 0 it is at x = +x_m.When t = 0.75T:

This plot shows a mass oscillating as x = x_m cos (ωt + φ) .What are x_m and φ?