Question

Average velocity of a particle executing SHM in one complete vibration is:
$\text{A}\text{. }{\displaystyle \frac{A\omega }{2}}$
$\text{B}\text{. }A\omega$
$\text{C}\text{. }{\displaystyle \frac{A{\omega }^2}{2}}$
$\text{D}\text{.}$ zero

Answer 1

- Hint – In one complete vibration, displacement of a particle will be zero, so to find the average velocity use the formula, average velocity = displacement / time.
Formula used- $v={\displaystyle \frac{s}{t}}$

Complete step-by-step solution -

Simple harmonic motion is a special type of periodic motion where the restoring force on the moving object is directly proportional to, and opposite of, the object’s displacement vector. It results in an oscillation. When a vibration or an oscillation repeats itself over and over the motion is called periodic.
Now as asked in the question, the average velocity of a particle executing SHM i.e., Simple Harmonic Motion in one complete vibration.
So, to find velocity we should use the formula, $v={\displaystyle \frac{s}{t}}$ , where v is the average velocity, s is the average displacement and t is the time.
So, now as we know that in one complete vibration, displacement of a particle will be zero, so the average velocity will be-
$v={\displaystyle \frac{s}{t}}={\displaystyle \frac{0}{t}}=0$
Therefore, the average velocity of a particle executing SHM in one complete vibration is zero.
Hence, the correct option is D.

Note- Whenever such types of questions appear, first know what is SHM, as mentioned in the solution, SHM is Simple Harmonic Motion, which is a special type of periodic motion. Then as we know average velocity can be found out by knowing the average displacement and since, average displacement in one complete vibration is zero, so the velocity will also be zero.