Question

A particle executing $SHM$. The phase difference between velocity and displacement is

• A. $0$
• B. $\frac{\pi}{2}$
• C. $\pi$
• D. $2\pi$

Answer 1

Answer: (B)

$\frac{\pi}{2}$

Answer 2

Let the displacement of a particle executing $SHM$ at any instant $t$ is,$x = Acos \omega t$ Velocity, $v = - A \omega cos \omega t = A \omega cos (\omega t + \frac{\pi}{2})$ Phase of displacement, $\phi _1 = \omega t$ Phase of velocity, $\phi _2= (\omega t + \frac{\pi}{2})$ $\therefore$ Phase difference $= \phi_{2}-\phi_{1}$ $= \omega t + \frac{\pi}{2} - \omega t = \frac{\pi}{2}$