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the period T of a rigid-body compound pendulum for small angles is given byT=2π√I/mgR

where I is the moment of inertia of the pendulum about the pivot point, m is the mass of the pendulum, and R is the distance between the pivot point and the center of mass of the pendulum.

For example, for a pendulum made of a rigid uniform rod of length L pivoted at its end, I = (1/3)mL2. The center of mass is located in the center of the rod, so R = L/2. Substituting these values into the above equation gives T = 2π√2L/3g. This shows that a rigid rod pendulum has the same period as a simple pendulum of 2/3 its length.

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Q: How Can a compound pendulum be treated as a simple pendulum?
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Differences between compound pendulum and simple pendulum?

Compound pendulum is a physical pendulum whereas a simple pendulum is ideal pendulum. The difference is that in simple pendulum centre of mass and centre of oscillation are at the same distance.


Why a compound pendulum is called equivalent simple pendulum?

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Is oscillation of compound pendulum or simple pendulum is perfectly simple harmonic motion?

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What are difference between simple pendulum and compound pendulum?

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applications of simple pendulum


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What is the difference between coupled pendulum and simple pendulum?

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What is the advantages of compound pendulum over simple pendulum?

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To determine the value of g acceleration due to gravity by means of a compound pendulum?

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