Question

The time period of body executing simple harmonic motion is $2s.$ After starting from $t=0$ time after how much time is displacement will be equal to the amplitude?

Answer 1

Given,

$T=2s,\therefore {\omega }_0=\frac{2\pi }{T}=\frac{2\pi }{2}=\pi rad{s}^{-1}$

$\therefore$ Equation and displacement of S.H.M.

$y=asin{\omega }_{0}t$

or $y=asin\pi t$

given , when $y=a,t=?$

$\therefore a=asin\pi t$

or $sin\pi t=1$

but $sin\frac{\pi }{2}=1$

$\therefore \pi t=\frac{\pi }{2}$

$\therefore t=\frac{1}{2}s$