Simple Pendulums in Simple Harmonic motion

Adel H. Alameh

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arXiv · 2605.24708

Simple Pendulums in Simple Harmonic motion

Adel H. Alameh

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Abstract

The motion of a simple pendulum in a uniform gravitational field can be described by the solution of a second-order differential equation, nonlinear differential equation. In practice we solve this equation using the small angle approximation relying on students familiarity with simple harmonic motion. This paper presents a straightforward method of finding the time equation of motion of a simple pendulum for small angular amplitudes, without having any recourse to solving the differential equation that governs its oscillations. This method relies on finding the indefinite integral of a certain relation derived from the conservation of mechanical energy of the system (Pendulum-Earth). And shows no need to the mathematical complexities in which differential equations are involved.

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Adel H. Alameh. 2026-05-23. Simple Pendulums in Simple Harmonic motion. https://arxiv.org/abs/2605.24708

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