Question

A particle performs a $S.H.M$. of amplitude $A$and period $T$. If the particle is half way between the mean position and the extreme position , then its speed at that point will be

• A. $\frac{\pi A\sqrt{3}}{T}$
• B. $\frac{3{\pi }^{2}A}{T}$
• C. $\frac{\pi A}{T}$
• D. $\frac{\pi A\sqrt{3}}{2T}$

Answer 1

The correct option is C $\frac{\pi A}{T}$

Given,

Displacement is half

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

$\omega t={\sin }^{-1}\left(\frac{1}{2}\right)=\frac{\pi }{6}$

$t=\frac{T}{12}$

Velocity, $v=\omega A\cos \omega t=\frac{2\pi }{T}A\cos (\frac{2\pi }{T}\times \frac{T}{6})$

$v=\frac{2\pi A}{T}\times \frac{1}{2}=\frac{\pi A}{T}$

Hence, velocity is $\frac{\pi A}{T}$