Question

A body is executing S.H.M. When its displacement from the mean position is $4cm$ and $5cm$, the corresponding velocity of the body is $10cm/sec$ and $8cm/sec$. then the time period of the body is

• A. $2\pi sec$
• B. $\pi /2sec$
• C. $\pi sec$
• D. $3\pi /2sec$

Answer 1

The correct option is C $\pi sec$

$\begin{array}{c}v=\omega \sqrt{A^2-x^2}\\ \Rightarrow 8=\omega \sqrt{A^2-25}\\ \&10=\omega \sqrt{A^2-16}\\ \Rightarrow {\left(\frac{8}{10}\right)}^2=\frac{A^2-25}{A^2-16}\\ \Rightarrow \frac{16}{25}=\frac{A^2-25}{A^2-16}\\ \Rightarrow 16A^2-256=25A^2-625\\ \Rightarrow 9A^2=369\\ A^2=41\\ \Rightarrow 8=\omega \sqrt{41-25}\\ \Rightarrow 8=4\omega \\ \therefore \omega =2=\frac{2\pi }{T}\\ T=\pi \sec \end{array}$

$\therefore$ Option $C$ is correct.