An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime
Physics Education
2010-03-12 v3
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.
Keywords
Cite
@article{arxiv.physics/0510206,
title = {An accurate formula for the period of a simple pendulum oscillating beyond the small-angle regime},
author = {F M S Lima and P Arun},
journal= {arXiv preprint arXiv:physics/0510206},
year = {2010}
}
Comments
15 pages and 4 figures. to appear in American Journal of Physics