Question

A particle performs SHM with a period $T$ and amplitude $A$. The mean velocity of the particle over the time interval during which it travels a distance $\frac{A}{2}$ from the extreme position is

• A. $\frac{A}{T}$
• B. $\frac{2A}{T}$
• C. $\frac{3A}{T}$
• D. $\frac{A}{2T}$

Answer 1

The correct option is C $\frac{3A}{T}$

Displacement of particle when starting from extreme position,
$x=\text{A cos}\omega t$
At $A/2$ from extreme position,
$\frac{A}{2}=\text{A cos}\omega t_o$
$\cos \frac{\pi }{3}=\text{cos}\omega t_o\frac{\pi }{3}=\omega t_o\therefore t_o=\frac{\pi }{3\omega }=\frac{T}{6}$
Mean velocity, $\overline{v}=\frac{\text{Total displacement}}{\text{Total time taken}}$
$\overline{v}=\frac{A/2}{T/6}=\frac{3A}{T}$