Question

Average velocity of a particle performing SHM in one time period is:
A. Zero
B. $\dfrac{{A\omega }}{2}$
C. $\dfrac{{A\omega }}{{2\pi }}$
D. $\dfrac{{2A\omega }}{\pi }$

Answer 1

A time period $(T)$ is defined as the time taken for one complete cycle of vibration to pass through a given point. To solve the given question first we need to find the displacement of the particle. Consider $x$ to be displacement, then apply the formula of average velocity.

Formula used:
${\text{Average velocity = }}\dfrac{{{\text{Total displacement}}}}{{{\text{Total time }}}}$

Complete step-by-step answer:
Let us assume that $x$ is the displacement of the particle. So, according to the question, after one time period, the particle returns back to its mean position as at the beginning of the time period. Thus, displacement is, $x = 0$
Therefore, ${\text{Average velocity = }}\dfrac{{{\text{Total displacement}}}}{{{\text{Total time }}}} = 0$

So, the correct answer is “Option A”.

Additional Information: Simple harmonic motion (SHM) is defined as the vibratory motion in a system in which the restoring force is proportional to the displacement from the equilibrium.
Characteristics of a simple harmonic motion is defined as:

1. The motion of the body is periodic.
2. The acceleration of the body is directly proportional to the displacement of the body. 3) Acceleration is always directed towards the equilibrium position.
   Time period of simple harmonic motion depends upon the mass of the object.

Note: A periodic motion is defined as the repeating motion after an equal interval of time. There is no equilibrium position and restoring force. The time period of the wave decreases as the frequency of the wave increases. Unit of time is “seconds”.