Question

A particle is performing linear S.H.M. with period 6 s and amplitude 'a'. The minimum time taken by the particle to travel between two points situated at a distance $\frac{a}{2}$ on either sides of mean position is :

• A. $1$ s
• B. $1.5$ s
• C. $3$ s
• D. $6$ s

Answer 1

The correct option is A $1$ s

Let the two points be A and B.

The particle first passes through A and then through B.

Phase at point A is $\frac{5\pi }{6}$ and at B is $\frac{7\pi }{6}$.
$x=A\sin \omega t\Rightarrow \omega t_1=\frac{5\pi }{6}and\omega t_2=\frac{7\pi }{6}\Rightarrow t_2-t_1=\frac{2\pi }{6\omega }=\frac{1}{6}\left(\frac{2\pi }{\omega }\right)=\frac{T}{6}=1s$