The amplitude and the periodic time of a $S.H.M.$ are $ 5\,cm$ and $6\,sec$ respectively. At a distance of $2.5\,cm$ away from the mean position, the phase will be
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The equation of motion is given as $y=5 \sin \frac{2 \pi t}{6}$
Here, $y=2.5 cm$
$\therefore 2.5=5 \sin \frac{2 \pi t}{6}$
$\Rightarrow \frac{\pi}{6}=\frac{2 \pi t}{6} \Rightarrow t=\frac{1}{2} s$
$\therefore$ The phase $=\frac{2 \pi t}{6}=\frac{2 \pi}{6} \times \frac{1}{2}=\frac{\pi}{6}$
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