Question

A simple harmonic motion has an amplitude A and time period T. Find the time required by it to travel directly from $x=0$ to $x=\frac{A}{\sqrt{2}}$.

Answer 1

$x=A\sin \left(\omega t\right)$ At $t=0,x=0$

$x=\frac{A}{\sqrt{2}}$

$\frac{A}{\sqrt{2}}=A\sin \left(\omega t\right)$

$\omega t=\frac{\pi }{4}$

$\frac{2\pi }{T}t=\frac{\pi }{4}$

$t=\frac{T}{8}$