Question

A particle performs a S.H.M. of amplitude 10 cm and period 12 s. What is the speed of the particle 3 s, after passing through its mean position?

Answer 1

Let the particle be at mean position initially.

Displacement of particle $x=A\sin wt$

Velocity of particle $v=\frac{dx}{dt}=Aw\cos wt$

where $A=10cm$, $w=\frac{2\pi }{T}=\frac{2\pi }{12}=\frac{\pi }{6}$

$⟹v=10\times \frac{\pi }{6}\cos \left(\frac{\pi t}{6}\right)$

At $t=3s$, $v=10\times \frac{\pi }{6}\cos (\frac{\pi }{6}\times 3)$

$⟹v=0$ $(\because \cos \frac{\pi }{2}=0)$