A particle executes $S.H.M.$ according to equation $x=10( cm ) \cos \left[2 \pi t+\frac{\pi}{2}\right]$, where $t$ is in second. The magnitude of the velocity of the particle at $t=\frac{1}{6} \,s$ will be .............. $cm / s$
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(D)
$x=10 \cos \left[2 \pi t+\frac{\pi}{2}\right]$
At $t=\frac{1}{6} s$
$x=10 \cos \left[\frac{\pi}{2}+\frac{\pi}{3}\right]$
$x=-10 \sin \frac{\pi}{3}$
$x=-5 \sqrt{3}$
$v=\omega \sqrt{A^2-x^2}$
$v=2 \pi \sqrt{100-75}$
$v=10 \pi$
$v=31.4 \,cm / s$
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