Question

Find the period of small oscillation of a simple pendulum of length ' $\ell$ ' if its point of suspension $O$ moves relative to the earth with a constant acceleration $\overline{a}$, given $\ell =30cm$ and $|\overline{a}|=g/2$ and the angle between the vectors $\overline{g}$ and $\overline{a}$ is $\beta =120^{\circ }$. The period (in $\sec$) of oscillation of the pendulum is

Answer 1

Answer: 0.95

$T=2\pi \sqrt{\frac{e}{g_{eff}}}$

$g_{\text{eff }}=\sqrt{g^2+\frac{g^2}{4}+2\left(\frac{g}{2}\right)g\cos 60^{\circ }}$
$g_{\text{eff }}=\sqrt{\frac{(4+1+2)g}{4}}=\sqrt{\frac{78}{4}}$
$T=2\pi \sqrt{\frac{\ell x^2}{\sqrt{7}g}}$
$T=2\pi \sqrt{\frac{2\times 0.3}{\sqrt{7}\times 10}}$
$T=0.95\sec$