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The phase difference between displacement and acceleration of a particle in a simple harmonic motion is:
(A) \(\pi \mathrm{rad}\)
B \(\frac{3 \pi}{2} \mathrm{rad}\)
C \(\frac{\pi}{2} \mathrm{rad}\)
D zero

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Solution:
$$
\begin{aligned}
&\text { Displacement }(\mathrm{x}) \text { of SHM } \\
&x=A \sin (\omega t+\phi) \ldots(i) \\
&\frac{d x}{d t}=A \omega \cos (\omega t+\phi) \\
&\text { Acceleration }(a)=\frac{d^{2} x}{d t^{2}} \\
&\Rightarrow a=-\omega^{2} A \sin (\omega t+\phi) \\
&\Rightarrow a=\omega^{2} A \sin (\omega t+\phi+\pi) \ldots(i i)
\end{aligned}
$$
from (1) \& (2), phase difference between displacement and acceleration is \(\pi\)
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