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 $\dots \dots \dots$

Answer 1

Answer: 7

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

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