Question

Starting from an 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. $1/6s$
• B. $1/3s$
• C. $1/4s$
• D. $1/12s$

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 $\omega t=\frac{\pi }{6}\Rightarrow t=\frac{\pi }{6\pi }=\frac{1}{6}s$