Question

physical meaning of equivalent length of compound pendulum

Answer 1

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⬆️⬆️⬆️⬆️⬆️⛔⛔⛔♦️♦️♦️Any swinging rigid body free to rotate about a fixed horizontal axis is called acompound pendulum or physical pendulum. The appropriate equivalent length for calculating the period of any such pendulum is the distance from the pivot to the center of oscillation.

Answer 2

The equivalent length of a compound pendulum decides the time period or the frequency of the pendulum.

Explanation:

• A rigid body of any shape and size that can oscillate freely about a horizontal axis passing through it and the perpendicular to the plane of the body is called a compound pendulum.
• For example, an alarm clock on the wall.
• Consider a rigid body of mass $m$ as shown in the following figure.
• It is suspended through the point O and oscillating through the axis passing through O and perpendicular to the plane of the paper. This is a general compound pendulum. Its center of mass is C.
• The distance between the suspension point (O) of the body and the center of mass (C) of the body is called equivalent length (L).
• This is the effective length (L) which decides the time period of the pendulum.
• It is represented by the formula:

        $\[\;T = 2\pi \sqrt {\frac{L}{g}} \]$

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