Question

If maximum speed of a particular in SHM is given by $V_m$. What is its average speed?

• A. $\frac{\pi V_m}{2}$
• B. $\frac{2V_m}{\pi }$
• C. $\frac{\pi V_m}{4}$
• D. $\frac{V_m}{\sqrt{2}}$

Answer 1

The correct option is B $\frac{2V_m}{\pi }$

Let the SHM be represented as $x=Asin(\omega t+\varphi )$

Thus the speed of a particle=$\frac{dx}{dt}=\left|A\omega cos\right(\omega t+\varphi \left)\right|$

$\Rightarrow V_m=A\omega$

The average speed of the particle=$\frac{{\int }_0^{\left(2\pi /\omega \right)}\left|A\omega cos\right(\omega t+\varphi \left)\right|}{2\pi /\omega }$

$=\frac{2A\omega }{\pi }$

$=\frac{2}{\pi }{V}_m$