Question

The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:

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

Answer 1

Answer: (A)

$\pi$ rad

Answer 2

Displacement (x) of SHM
$x=A\,sin \left(\omega t+\phi\right) \dots(i)$
$\frac{dx}{dt}=A\,\omega\,cos(\omega\,t+\phi)$
Acceleration $(a)=\frac{d^{2}x}{dt^{2}}$
$\Rightarrow a=-\omega^{2}\,A\,sin(\omega\,t+\phi)$
$\Rightarrow a=\omega^{2}\,A\,sin(\omega\,t+\phi+\pi)\dots(ii)$
from (1) & (2), phase difference between displacement and acceleration is $\pi$