Fifth-order AGM-formula for the period of a large-angle pendulum

نویسندگان

چکیده

In this paper, an approximate algebraic formula for calculating the period of a large-angle pendulum was developed based on fifth-order iteration arithmetic-geometric mean (AGM) complete elliptic integral first kind. The present is capable estimating nonlinear entire range possible amplitudes i.e. 0∘<A<180∘, but it particularly useful (90∘<A≤170∘) and extremely (170∘<A≤179.9∘) oscillations. accuracy tested using exact solution, numerical solution other published formulas. It observed that several orders more accurate than maximum error up to 179.9∘ found be 2.93×10-6%. can used pedagogical purpose because its simplicity.

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ژورنال

عنوان ژورنال: Revista Brasileira de Ensino de Física

سال: 2023

ISSN: ['1806-1117', '1806-9126']

DOI: https://doi.org/10.1590/1806-9126-rbef-2023-0014