A particle executes $S.H.M.$ and its position varies with time as $x=A$ sin $\omega t$. Its average speed during its motion from mean position to mid-point of mean and extreme position is
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(b)
Phase at mean position $=0$
Phase at mid point
$\frac{A}{2}=A \sin \phi$
$\phi=\frac{\pi}{6}$
Time it takes to travel a phase difference of $\phi$
$t=\frac{2 \pi}{\omega} \times \frac{\phi}{2 \pi}$
or $t=\frac{\phi}{\omega}$
or $t=\frac{\pi}{6 \omega}$
Average speed $=\frac{\text { Total distance }}{\text { Time taken }}$
$=\frac{A / 2}{\pi / 6 \omega}$
$=\frac{3 A \omega}{\pi}$
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