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 $\ell=30\, cm$ 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

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

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