Question

Time period of a simple pendulum is $T$. The time taken to complete $5 / 8$ oscillations starting from mean position is $\frac{\alpha}{\beta} T$. The value of $\alpha$ is $\ldots \ldots \ldots$

Answer 1

$\frac{5}{8}$ th of oscillation $=\left(\frac{1}{2}+\frac{1}{8}\right)^{\text {th }}$ of oscillation

$\pi+\theta=\omega t$
$\pi+\frac{\pi}{6}=\left(\frac{2 \pi}{T}\right) t$
$\frac{7 \pi}{6}=\left(\frac{2 \pi}{T}\right) t$
$t=\frac{7 T}{12}$