Abstract:In this paper, an approximate algebraic formula for calculating the period of a large-angle pendulum was developed based on fifth-order iteration of the arithmetic-geometric mean (AGM) formula for the complete elliptic integral of the first kind. The present formula is capable of estimating the period of the nonlinear pendulum for the entire range of possible amplitudes i.e. 0 • < A < 180 • , but it is particularly useful for large-angle (90 • < A ≤ 170 • ) and extremely large-angle (170 • < A ≤ 179.9 • ) osci… Show more
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