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Question

# Show that the expression for the period of a physical pendulum reduces to that of a simple pendulum if the physical pendulum consists of a particle with mass $m$ on the end of a massless string of length $L$.

Solution

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A physical pendulum is pivoted at a fixed point. When the pendulum is in its equilibrium position, then its center of mass is directly under its pivot point. However, when it is displaced from equilibrium by an angle $\theta$, a restoring torque acts on it in the opposite direction of its motion.

\begin{align*} \tau &=-\left( mg \right)\left( L\sin \theta \right)\\ \end{align*}

Where,

$m=$ mass of physical pendulum

$L=$ distance of pivot point from center of mass

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