Question

A simple harmonic motion has an amplitude A and time period T. Find the time required by it to travel directly from $x=A$ to $x=A/2$.

Answer 1

$x=A\sin \left(\frac{2\pi }{T}t\right)$

when $x=0$ then

$\Rightarrow 0=A\sin \left(\frac{2\pi }{T}t\right)$

$\Rightarrow t=0$

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

$\Rightarrow \frac{A}{2}=A\sin \left(\frac{2\pi }{T}t\right)$

$\Rightarrow \frac{2\pi t}{T}=\frac{\pi }{6}$

$\Rightarrow t=\frac{T}{12}sec.$

Hence, the answer is $\frac{T}{12}sec.$