Question

A particle is performing SHM as $x=cos(\pi t+\frac{3\pi }{2})$. What is the time period, phase and displacement of the particle at $t=1second$.

• A. $1s,\pi /2,1$
• B. $2s,\pi /2,0$
• C. $1s,3\pi /2,0$
• D. $2s,3\pi /2,1/2$

Answer 1

Answer: (B)

$2s,\pi /2,0$

The displacement of he particle performing SHM is:

$x=a\sin (\omega t+\varphi )$

Where,

a $=$ Amplitude

$\omega =$ Angular frequency

t $=$ Time

$\varphi =$ Phase angle

We have been given,

$x=\cos (\pi t+\frac{3\pi }{2})$ $(\therefore \cos \theta =\left(\sin \theta +\frac{\pi }{2}\right))$

$x=\sin (\pi t+\frac{\pi }{2}+\frac{3\pi }{2})$

$x=\sin (\pi t+2\pi )$

$\therefore a=1m$

$\omega =\pi rad/s$

$\varphi =2\pi$

$T=\frac{2\pi }{\omega }=2s$

$x=0$ (at t $=$ 1s) $=\sin (\pi +2\pi )=\sin 3\pi$