Question

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

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

Answer 1

The correct option is B $\frac{\pi }{2}$

Let the displacement of a particle executing SHM at any instant t is, $x=Acos\omega t$
Velocity, $v=-A\omega sin\omega t=A\omega cos[\omega t+\frac{\pi }{2}]$
Phase of displacement, ${\varphi }_1=\omega t$
Phase of velocity, ${\varphi }_2=[\omega t+\frac{\pi }{2}]$
Phase difference = ${\varphi }_2-{\varphi }_1=\omega t+\frac{\pi }{2}-\omega t=\frac{\pi }{2}$