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

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

Oscillations

Solution:

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} $
$= \omega t + \frac{\pi}{2} - \omega t = \frac{\pi}{2}$