Question
The phase difference between displacement and acceleration of a particle in a simple harmonic motlon is
✓
Answer
Displacement $(x)$ equation of $SHM$
$x = A \sin (\omega t +\phi)$ $....(1)$
$\frac{ dx }{ dt }= A \omega \cos (\omega t +\phi)$
acceleration $(a)=\frac{d^{2} x}{d t^{2}}$
$a=-\omega^{2} A \sin (\omega t+\phi)$
$a =\omega^{2} A \sin (\omega t +\phi+\pi)$$.....(2)$
from $(1) \;and\;(2),$ phase difference between displacement and acceleration is $\pi .$
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