Question

What is phase difference between displacement and acceleration of a particle executing simple harmonic motion

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

Answer 1

The correct option is C $\pi$

$Y=asin(wt+\theta )$

on differentiation$,$

$v=awcos(wt+\theta )$

again differentiation u will get$,$

$a=-a{w}^{2}sin(wt+\theta )$

now take the minus sign inside as$\pi$

$a=a{w}^{2}sin(wt+\theta +\pi )$

So phase difference between displacement and acceleration will be$,$

= wt + \theta + π —{ wt + \theta }

$=wt+\theta +\pi -wt-\theta$

$=\pi$

Hence,

option $\left(C\right)$ is correct answer.