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

The Correct Option is A

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 $\pi$