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obtain the expression for time period of simple pendulum performing shm.
Asked by rustampathan | 25 Feb, 2024, 06:39: PM

Figure shows a simple pendulum that has length and mass of bob is m.

If a small angular displacement θ is made as shown in figure , the torque τ on the bob is

.......................(1)

where g is acceleration due to gravity . Negative sign indicates the torque is in clockwise direction.

By Newton's second law , Torque τ acting on body is

........................(2)

where is moment of inertia and α is angular acceleration .

By equating (1) and (2) and after simplification, we get

........................ (3)

Above equation is equation of SHM , i.e. acceleration is proportional to displacement .

Proportionality constant in eqn.(3) is  square of angular speed , i.e.,

Hence , we get

From above expression, we get period T of simple pendulum as

Answered by Thiyagarajan K | 25 Feb, 2024, 08:50: PM

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