Question

A simple pendulum of length $1m$ is oscillating with an angular frequency $10rad/s$. The support of the pendulum starts oscillating up and down with a small angular frequency of $1rad/s$ and an amplitude of $10^{-2}m$. The relative change in the angular frequency of the pendulum is best given by :

• A. $10^{-3}rad/s$
• B. $10^{-1}rad/s$
• C. $1rad/s$
• D. $10^{-5}rad/s$

Answer 1

Answer: (A)

Angular frequency of pendulum
$\omega =\sqrt{\frac{g_{eff}}{\ell }}$
$\therefore \frac{\Delta \omega }{\omega }=\frac{1}{2}\frac{\Delta g_{eff}}{g_{eff}}$
$\Delta \omega =\frac{1}{2}\frac{\Delta g}{g}\times \omega$
[${\omega }_s$ = angular frequency of support] $\Delta \omega =\frac{1}{2}\times \frac{2A{\omega }_s^2}{100}\times 100$
$\Delta \omega =10^{-3}$ rad/sec.