Question

Find the velocity when $KE=PE$ of the body undergoing SHM, $\text{Amplitude}=x_0$ and angular frequency is $\omega$. How many times in a cycle $KE=PE$ ?

• A. $\frac{\omega x_0}{\sqrt{2}},2$
• B. $\omega x_0,2$
• C. $\frac{\omega x_0}{\sqrt{2}},4$
• D. $\omega x_0,4$

Answer 1

Answer: (C)

$\frac{\omega x_0}{\sqrt{2}},4$

Equating KE and PE, we get,
$\frac{1}{2}k{x}^2=\frac{1}{2}k(x_0^2-x^2)$, we get
$x=\frac{x_0}{\sqrt{2}}$
$\therefore v=\frac{\omega x_0}{\sqrt{2}}$
Also,$x=\frac{x_0}{\sqrt{2}}$ occurs 4 times in one cycle, hence option C is correct.