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 2 L /3 directly below the fi

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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 2 L /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?

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Ans. (D) T ′ = 4 T 1 ​ ​ + 4 T 2 ​ ​ + 4 T 2 ​ ​ + 4 T 1 ​ ​ = 2 T 1 ​ ​ + 2 T 2 ​ ​ T 1 ​ = 2 π g L ​ ​ , T 2 ​ = 2 π 3 g L ​ ​

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