An improved 'heuristic' approximation for the period of a nonlinear pendulum: Linear analysis of a classical nonlinear problem

作者：Belendez A^*; Hernandez A; Belendez T; Marquez A; Neipp C

来源：International Journal of Nonlinear Sciences and Numerical Simulation, 2007, 8(3): 329-334.

DOI：10.1515/IJNSNS.2007.8.3.329

• nonlinear oscillator
• simple pendulum
• large-angle period
• approximate solutions

A new analytical approximate expression for the period of the simple pendulum is obtained by using a heuristic but pedagogical derivation. This formula depends on two parameters obtained by comparing term-by-term the power-series expansions of the approximate and exact expressions for the period. This formula is compared with others in the literature and the numerical results obtained show that the published approximations are not nearly as good as the new expression proposed in this paper.

• 出版日期2007