A simple pendulum of length L oscillates with a small angular displacement θ . The horizontal displacement of the bob from its equilibrium position is approximately given by:

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Let the horizontal displacement of the bob from its equilibrium position be $x$ . From trigonometry, $x = L sin θ$ .

For small angular displacements $θ$ (measured in radians), the small angle approximation states that $sin θ \approx θ$ . Therefore, the horizontal displacement $x \approx L θ$ .

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