A simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed a distance $2L/3$ directly below the fixed pivot point so that the pendulum would swing as shown in the figure below. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?
A simple pendulum of length $L$ is constructed from a point object of mass $m$ suspended by a massless string attached to a fixed pivot point. $A$ small peg is placed a distance $2L/3$ directly below the fixed pivot point so that the pendulum would swing as shown in the figure below. The mass is displaced $5$ degrees from the vertical and released. How long does it take to return to its starting position?
- A
$\pi \sqrt {\frac{L}{g}} \left( {1 + \sqrt {\frac{2}{3}} } \right)$
- B
$\pi \sqrt {\frac{L}{g}} \left( {2 + \sqrt {\frac{2}{3}} } \right)$
- C
$\pi \sqrt {\frac{L}{g}} \left( {1 + \frac{1}{3}} \right)$
- D
$\pi \sqrt {\frac{L}{g}} \left( {1 + \frac{1}{{\sqrt 3 }}} \right)$
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