Question

What is the phase difference (in radians) between velocity and displacement of a particle performing SHM at any time $t>0$.

• A. $0$
• B. $\frac{\pi }{2}$
• C. $\pi$
• D. $\frac{3\pi }{2}$

Answer 1

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

A general SHM is represented by sinusoidal motion $x=A\sin (\omega t+{\varphi }_0)$

Thus, velocity is give by $v=\frac{dx}{dt}=A\omega \cos (\omega t+{\varphi }_0)=A\omega \sin (\omega t+{\varphi }_0-\pi /2)$

Thus, the phase of displacement is ${\varphi }_{\text{disp}}=\omega t+{\varphi }_0$

and, the phase of velocity is ${\varphi }_{\text{vel}}=\omega t+{\varphi }_0-\pi /2$

Phase difference is $|{\varphi }_{\text{disp}}-{\varphi }_{\text{vel}}|=\pi /2$