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 $a/2$ 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 $\frac{3a}{T}$

As particle starts from extreme position,
We can consider equation opf SHM as
$y=a\cos \omega t$
when it travels $a/2$ from mean position, we get
$\frac{1}{2}=\cos \omega t$
$t=\frac{\pi }{3\omega }$
$t=\frac{T}{6}$
Average velocity is
$\therefore V_{avg}=\frac{\frac{a}{2}}{\frac{T}{6}}=\frac{3a}{T}$