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An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime

F M S Lima·P Arun
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Abstract

A simple approximation formula is derived here for the dependence of the period of a simple pendulum on amplitude that only requires a pocket calculator and furnishes an error of less than 0.25% with respect to the exact period. It is shown that this formula describes the increase of the pendulum period with amplitude better than other simple formulas found in literature. A good agreement with experimental data for a low air-resistance pendulum is also verified and it suggests, together with the current availability/precision of timers and detectors, that the proposed formula is useful for extending the pendulum experiment beyond the usual small-angle oscillations.

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F M S Lima, P Arun. 2005-10-23. An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime. https://doi.org/10.1119/1.2215616

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