Question

The periodic time of a body executing SHM is $4s$. After how much interval from time $t=0$, its displacement will be half of its amplitude?

• A. $1/2s$
• B. $1/3s$
• C. $1/4s$
• D. $1/6s$

Answer 1

The correct option is B $1/3s$

Given,

$T=4sec$

Displacement equation is S.H.M is given by

$y=asin\omega t$. . . . . .(1)

If $y=\frac{a}{2}$

Equation (1) becomes,

$\frac{a}{2}=asin\omega t$

$sin\omega t=0.5$

$\omega t=si{n}^{-1}\left(0.5\right)=\frac{\pi }{6}$

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

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

$t=\frac{4}{12}$

$t=\frac{1}{3}sec$

The correct option is B.