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 $v=31.4cm/s$