An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime
arXiv:physics/0510206 · doi:10.1119/1.2215616
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.
15 pages and 4 figures. to appear in American Journal of Physics