Question

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

• A. Zero
• B. $\frac{3 A \omega}{\pi}$
• C. $\frac{A \omega}{2 \pi}$
• D. $\frac{2 A \omega}{\pi}$

Answer 1

Answer: (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 }} $
$=\frac{A / 2}{\pi / 6 \omega}$
$=\frac{3 A \omega}{\pi}$