Question 166 of 194

Time period of a simple pendulum is $T$. The time taken to complete $\dfrac{5}{8}$ oscillations starting from mean position is $\dfrac{\alpha }{12}T$. The value of $\alpha$ is ______.

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Answer: 7

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

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