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| Main Author: | |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2605.24708 |
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| _version_ | 1866914596975017984 |
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| author | Alameh, Adel H. |
| author_facet | Alameh, Adel H. |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2605_24708 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Simple Pendulums in Simple Harmonic motion Alameh, Adel H. Classical Physics 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. |
| title | Simple Pendulums in Simple Harmonic motion |
| topic | Classical Physics |
| url | https://arxiv.org/abs/2605.24708 |