Question

The phase difference between displacement and velocity of a particle in simple harmonic motion is

• A. \( \pi \, \text{rad} \)
• B. \( \frac{3\pi}{2} \, \text{rad} \)
• C. zero
• D. \( \frac{\pi}{2} \, \text{rad} \)

Hint:

In simple harmonic motion, the velocity is always \( \frac{\pi}{2} \) radians ahead of the displacement in phase. This is because the velocity is the derivative of displacement with respect to time.

Answer 1

The Correct Option is D

In simple harmonic motion (SHM), the displacement \( x \) and velocity \( v \) of a particle are related by the following equations: \[ x(t) = A \cos(\omega t + \phi) \] \[ v(t) = -A\omega \sin(\omega t + \phi) \] The velocity is the time derivative of displacement, and the phase difference between displacement and velocity arises because velocity leads displacement by \( \frac{\pi}{2} \, \text{rad} \).
Thus, the phase difference between displacement and velocity in SHM is \( \frac{\pi}{2} \, \text{rad} \).