# A simple pendulum of length 1 m is oscillating with an angular frequency of 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 :

$\\\text{Angular freq. of pendulum} \\ \\\omega=\sqrt{\frac{\mathrm{g}_{\mathrm{eft}}}{\ell}} \\\\ \frac{\Delta \omega}{\omega}=\frac{1}{2} \frac{\Delta \mathrm{g}_{\mathrm{eff}}}{\mathrm{g}_{\mathrm{eff.}}} \\\\ \Delta \omega=\frac{1}{2} \frac{\Delta \mathrm{g}}{\mathrm{g}} \times \omega\\\\ \Delta \omega=\frac{1}{2} \frac{\left(2 \mathrm{A} \omega_{\mathrm{s}}^{2}\right)}{100} \times 100 =10^{-3} \mathrm{rad} / \mathrm{sec} \\ \\ \omega_{\mathrm{s}}= Angular freq. of support.$

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