Question 1

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

Accepted Answer

E

Question 2

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

A

Question 3

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 4

In simple harmonic motion, the magnitude of the acceleration is greatest when:

Accepted Answer

The acceleration in simple harmonic motion is given by a = -ω^2x, where ω is the angular frequency and x is the displacement. The magnitude of the acceleration is proportional to both ω^2 and x. At the maximum displacement, the value of x is the greatest, resulting in the greatest magnitude of acceleration.

Question 5

The amplitude of any oscillator can be doubled by:

Accepted Answer

The amplitude of an oscillator is determined by both the initial displacement and initial speed. Therefore, doubling both initial displacement and initial speed will result in a doubling of the amplitude.

Question 6

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

Accepted Answer

Frequency = Number of Vibrations / Time
Frequency = 20 / 10 seconds
Frequency = 2 Hz

Question 7

Frequency f and angular frequency $ \omega $ 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 8

An oscillatory motion must be simple harmonic if:

Accepted Answer

Simple harmonic motion is characterized by an acceleration that varies sinusoidally with time. Therefore, choice D is the only option that correctly describes a necessary condition for simple harmonic motion. The other choices are not sufficient conditions for simple harmonic motion.

Question 9

In simple harmonic motion:

Accepted Answer

The answer of In simple harmonic motion:
...

Question 10

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 11

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

Accepted Answer

Both the initial displacement and velocity of the oscillator determine its amplitude and phase constant. The initial displacement determines the amplitude, and the initial velocity determines the phase constant.

Question 12

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

Accepted Answer

In simple harmonic motion, the displacement is maximum when the velocity is zero. This occurs at the points of maximum displacement from the equilibrium position, where the direction of motion changes from one direction to the other, resulting in the velocity being momentarily zero.

Question 13

A particle oscillating in simple harmonic motion is:

Accepted Answer

A particle oscillating in simple harmonic motion experiences a restoring force that is proportional to its displacement from equilibrium. At the ends of its path, the particle momentarily comes to rest before changing direction, and its velocity is therefore zero. However, its acceleration is at a maximum because it is accelerating towards the equilibrium position. At the center of its path, the particle is at equilibrium and the net force acting on it is zero, so its acceleration is also zero. Therefore, the particle is in equilibrium at the center of its path.

Question 14

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

Accepted Answer

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

Question 15

In simple harmonic motion, the magnitude of the acceleration is:

Accepted Answer

In simple harmonic motion, the magnitude of the acceleration is proportional to the displacement from the equilibrium position. This can be expressed by the equation a = -ω^2x, where a is acceleration, x is displacement, and ω is the angular frequency of the motion. This means that the acceleration increases as the displacement increases, and is zero at the equilibrium position.

Question 16

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

The answer of A particle is in simple harmonic motion...

Question 17

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 amplitude is half the distance between the limits of motion, so it is (50-10)/2 = 20 cm.
The frequency is the inverse of the period, which can be found by T=2*(time to go from one extreme to the other) = 0.5 s. Therefore, frequency = 1/T = 1/0.5 = 2 Hz.
Thus, the correct choice is B.

Question 18

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 19

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 20

A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. At which of the following times is it furthest from the equilibrium point?

Accepted Answer

The answer of A particle is in simple harmonic motion...

Quiz 15: Oscillations

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

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:

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

In simple harmonic motion, the magnitude of the acceleration is greatest when:

The amplitude of any oscillator can be doubled by:

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

Frequency f and angular frequency $\omega$ are related by

An oscillatory motion must be simple harmonic if:

In simple harmonic motion:

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:

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

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

A particle oscillating in simple harmonic motion is:

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

In simple harmonic motion, the magnitude of the acceleration is:

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:

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:

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

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

A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. At which of the following times is it furthest from the equilibrium point?

Quiz 15: Oscillations

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

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:

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

In simple harmonic motion, the magnitude of the acceleration is greatest when:

The amplitude of any oscillator can be doubled by:

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

Frequency f and angular frequency ω \omega ω are related by

An oscillatory motion must be simple harmonic if:

In simple harmonic motion:

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:

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

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

A particle oscillating in simple harmonic motion is:

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

In simple harmonic motion, the magnitude of the acceleration is:

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:

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:

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

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

A particle is in simple harmonic motion with period T. At time t = 0 it is at the equilibrium point. At which of the following times is it furthest from the equilibrium point?

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:

Frequency f and angular frequency $\omega$ are related by