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)

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, ${\varphi }_1=\omega t$
Phase of velocity, ${\varphi }_2=(\omega t+\frac{\pi }{2})$
$\therefore$ Phase difference $={\varphi }_2-{\varphi }_1$
$=\omega t+\frac{\pi }{2}-\omega t=\frac{\pi }{2}$