Question

A particle undergoes SHM with a time period of $2$ seconds. In how much time will it travel from its mean position to a displacement equal to half of its amplitude?

• A. $\left(1/2\right)s$
• B. $\left(1/3\right)s$
• C. $\left(1/4\right)s$
• D. $\left(1/6\right)s$

Answer 1

The correct option is D $\left(1/6\right)s$

Given,

$T=2sec$

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

The general equation is given by

$x=Asin\omega t$

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

$\omega t=\frac{\pi }{6}$

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

$t=\frac{1}{6}sec$

The correct option is D.