Question

A simple pendulum of length $1\, m$ is oscillating with an angular frequency $10\, rad/s$. The support of the pendulum starts oscillating up and down with a small angular frequency of $1 \,rad/s$ 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. $1\, rad/s$
• D. $10^{-5} rad/s$

Answer 1

Answer: (A)

$10^{-3} rad/s$

Answer 2

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] $\Delta \omega = \frac{1}{2} \times\frac{2 A \omega^{2}_{s} }{100} \times100$
$\Delta\omega = 10^{-3}$ rad/sec.