Question

A simple pendulum is released when $\theta =\pi /6$. The time period of oscillation is

• A. $2\pi \sqrt{\frac{l}{g}}$
• B. $2\pi \sqrt{\frac{l}{g}}\left(\frac{293}{288}\right)$
• C. $2\pi \sqrt{\frac{l}{g}}\left(\frac{288}{293}\right)$
• D. none of these

Answer 1

The correct option is B $2\pi \sqrt{\frac{l}{g}}\left(\frac{293}{288}\right)$

For large amplitudes, the time period is given by
$T=2\pi \sqrt{\frac{L}{g}}(1+\frac{{\theta }^2}{16})$
Substitute $\theta =\frac{\pi }{6}$, we get answer as
$T=2\pi \sqrt{\frac{L}{g}}\left(\frac{293}{288}\right)$
Option B is correct.