Question

Starting from origin, a body oscillates simple harmonically with a period of $2s$. After what time will its kinetic energy be $75\%$ of the total energy ?

• A. 1/6 s
• B. 1/12 s
• C. 1/3 s
• D. 1/4 s

Answer 1

Answer: (A)

As per,
$KE=\frac{75}{100}E=\frac{75}{100}\times \frac{1}{2}m{a}^2{\omega }^2$
$\frac{1}{2}m{a}^2{\omega }^2{\cos }^2\omega t=\frac{75}{100}\times \frac{1}{2}m{a}^2{\omega }^2$
${\cos }^2\omega t=\frac{3}{4}$
$\cos \omega t=\frac{\sqrt{3}}{2}=\cos \frac{\pi }{6}$
or $\omega t=\frac{\pi }{6}$
$\Rightarrow t=\frac{\pi }{6\pi }=\frac{1}{6}s$