Question

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

• A. 24.7 cm/s
• B. 20.5 cm/s
• C. 28.3 cm/s
• D. 31.4 cm/s

Answer 1

Answer: (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 $
or $ v=31.4 \,cm / s$