Solve this following
Question:

Time period of a simple pendulum is $\mathrm{T}$. The time taken to complete $5 / 8$ oscillations

starting from mean position is $\frac{\alpha}{\beta} \mathrm{T}$. The value of $\alpha$ is ………

 

Solution:

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

$\pi+\theta=\omega t$

$\pi+\frac{\pi}{6}=\left(\frac{2 \pi}{T}\right) \mathrm{t}$

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

$t=\frac{7 \mathrm{~T}}{12}$

 

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