Question

A simple pendulum of length $2$m with a bob of mass $m$ oscillates with an angular amplitudes of $\frac{\pi }{6}$ radians then find the tension in the string. (use $\sqrt{g}=\pi )$.

Answer 1

Length of bob $l=2m$

Angular amplitude of bob ${\theta }_0=\frac{\pi }{6}$

From figure, tension of string at any position which makes an angle $\theta$ with vertical is $T=mg\cos \theta$

So, $T$ at extreme position $T=mg\cos \frac{\pi }{6}$

$\Rightarrow T=m\times {\pi }^2\times \frac{\sqrt{3}}{2}$

$\Rightarrow T=\frac{\sqrt{3}{\pi }^{2}m}{2}$

At mean position $\theta =0$ $T=mg$

$\Rightarrow T={\pi }^{2}m$