Question

A particle undergoing SHM follows the position-time equation given as x = A sin $(\omega t+\frac{\pi}{3})$ . If the SHM motion has a time period of T, then velocity will be maximum at time $t=\frac{T}{β}$ for first time after t = 0. Value of β is equal to

Answer 1

The correct answer is 3.
x = A sin $(\omega t+\frac{\pi}{3})$
$⇒$v = $A\omega\cos(\omega t+\frac{\pi}{3})$
For maximum value of v
$\cos(\omega t+\frac{\pi}{3})=±1$
$⇒ \omega t+\frac{\pi}{3}=\pi$ ( for nearest value of t )
$\omega t=\frac{2\pi}{3}$
$t=\frac{T}{3}$
So , $\beta=3$