Question

A particle performs SHM on the x-axis with amplitude A and time period T. The time taken by the particle to travel a distance $\frac{A}{5}$ starting from rest is:

• A. $\frac{T}{20}$
• B. $\frac{T}{2\pi }$${\cos }^{-1}$ $\left(\frac{4}{5}\right)$
• C. $\frac{T}{2\pi }$${\cos }^{-1}$ $\left(\frac{1}{5}\right)$
• D. $\frac{T}{2\pi }$${\sin }^{-1}$$\left(\frac{1}{5}\right)$

Answer 1

The correct option is C $\frac{T}{2\pi }$${\cos }^{-1}$ $\left(\frac{1}{5}\right)$

Starting from the rest equation of sum is,

$X=A\cos \omega t$

At ,$x=\frac{A}{5}$

$\frac{A}{5}=A\cos \left(\frac{2\pi }{T}t\right)$

$\cos \left(\frac{2\pi }{T}t\right)=\frac{1}{5}$

$t=\frac{T}{2\pi }{\cos }^{-1}\left(\frac{1}{5}\right)$