Question

A particle is performing S.H.M. starting from extreme position. Graphical representation shows that, between displacement and acceleration, there is a phase difference of

• A. $0rad$
• B. $\frac{\pi }{4}rad$
• C. $\frac{\pi }{2}rad$
• D. $\pi rad$

Answer 1

The correct option is D $\pi rad$

Displacement of the particle executing SHM is given by $x=A\cos wt$

Differentiating it w.r.t. time we get $v=\frac{dx}{dt}=-Aw\sin wt$

Differentiating it again w.r.t. time we get acceleration as $a=\frac{dv}{dt}=-A{w}^2\cos wt$

$⟹$ $a=A{w}^2\cos (wt+\pi )$

Thus phase difference between displacement and acceleration is $\pi$ radian.