1) A body of mass 0.3 kg hangs by a spring with a force constant of 50N/m . The amplitude of oscillations is damped and reaches $\frac{1}{e}$ of its original value in about 100 oscillations. If $\omega$ and $\omega'$ are the angular frequencies of undamped and damped oscillations respectively , then percentage of $\left(\frac{\omega-\omega'}{\omega}\right)$ is A) $\left(\frac{1}{800 \pi}\right)$ B) $\left(\frac{\pi^{2}}{600 }\right)$ C) $\left(\frac{1}{800\pi^{2} }\right)$ D) $\left(\frac{\pi}{400 }\right)$ Answer: Option CExplanation:Hint The dispalcement of a spring mass oscillator , $X= Ae^{-bt/2m} \cos (\omega't+\phi)$ where, $\omega'$ = angular freequency of damped oscillation and $\omega'= \omega_{0}\sqrt{1-\frac{b^{2}}{4m^{2}\omega_{0}^{2}}}$
