Question

A particle performs simple harmonic motion with amplitude A and time period T. The mean velocity of the particle over the time internal during which it travels a distance of A/2 starting from 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 $\frac{3A}{T}$

Time interval T/6
$\Rightarrow$ Mean velocity $=\frac{{\int }_0^{T/6}vdt}{T/6}$
$\Rightarrow \frac{{\int }_0^{T/6}-Awsinwtdt}{T/6}={\left[\frac{6A}{T}coswt\right]}^{T/6}=\frac{-3A}{T}$