Question

A particle in SHM has maximum velocity $V_{max}$ at mean position and amplitude r. Its velocity when the displacement is 1/3 amplitude is

• A. $\left(2/3\right)V_{max}$
• B. $\sqrt{\left(2/3\right)}{V}_{max}$
• C. $\left(\sqrt{2}/3\right)max$
• D. $\left(2\sqrt{2}/3\right)V_{max}$

Answer 1

The correct option is D $\left(2\sqrt{2}/3\right)V_{max}$

$\begin{array}{c}V=w\sqrt{A^2-x^2}\\ \Rightarrow V=wA\sqrt{1-\frac{x^2}{A^2}}\\ \Rightarrow V=V_{max}\sqrt{1-\frac{r^2}{9r^2}}\\ V=V_{max}\left(\frac{2\sqrt{2}}{3}\right)\\ Hence,\\ optionDiscorrectanswer.\end{array}$