Question

A simple harmonic motion has an amplitude $A$ and time period $T$. The time required by it to travel $x=A$ to $x=\frac{A}{2}$ is:

• A. $T/6$
• B. $T/4$
• C. $T/3$
• D. $T/2$

Answer 1

The correct option is A $T/6$

$x=A\cos \omega t$

$t=0,x=A$

At $x=\frac{A}{2}$,

$\frac{A}{2}=A\cos \omega t$

$\omega t=\frac{\pi }{3}$

$\frac{2\pi }{T}t=\frac{\pi }{3}$

$t=\frac{T}{6}$ where T is time period