Systematic approximations for the period of a finite amplitude pendulum

Abstract

The standard series expansion for the period of a finite amplitude pendulum as a function of energy (and hence amplitude) provides a lower limit on the period when the series is truncated. An adjustment to the last term in the truncated series to take account of the dropped terms improves the accuracy of the approximation and provides an upper limit on the period. More accurate approximations can then be obtained using intermediate expressions.