Q: A particle is executing SHM. It passes through mean position at the instant t = 0. At what instants the speed of it is 50% of its maximum speed ?

Sol: $\large v = v_{max}cos\omega t $

$\large \frac{v_{max}}{2} = v_{max}cos(\frac{2\pi}{T} t) $

$\large t = \frac{T}{2\pi} cos^{-1}(\pm \frac{1}{2}) $