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The phase difference between displacement and velocity of a particle in simple harmonic motion is
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$\pi / 2 \mathrm{rad}$
The displacement of a particle executing SHM is
$x=A \sin \omega t$
$\therefore$ Velocity, $v=\frac{d x}{d t}=A \omega \cos \omega t$
$\therefore v=A \omega \sin \left(\omega t+\frac{\pi}{2}\right)$
$\therefore$ Phase difference, $\Delta \phi=\left(\omega t+\frac{\pi}{2}\right)-\omega t=\frac{\pi}{2} \mathrm{rad}$.
$x=A \sin \omega t$
$\therefore$ Velocity, $v=\frac{d x}{d t}=A \omega \cos \omega t$
$\therefore v=A \omega \sin \left(\omega t+\frac{\pi}{2}\right)$
$\therefore$ Phase difference, $\Delta \phi=\left(\omega t+\frac{\pi}{2}\right)-\omega t=\frac{\pi}{2} \mathrm{rad}$.
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