Nonlinear oscillation of the bifilar pendulum: an analytical approximation

Purpose The purpose of this paper is to present an analytical approximate solution of the nonlinear mathematical model of the bifilar pendulum. Design/methodology/approach First, the equation of motion derived based on the classical dynamics law by only an angular oscillation assumption and vertical oscillation is neglected. The energy balance method is applied to solve an established model and an analytical formulation has been obtained for the nonlinear frequency of the bifilar pendulum. Findings A comparison of results with those obtained by a numerical solution of the exact model (without any simplifications) shows the precise accuracy even for a large amplitude of oscillation. Originality/value The proposed model and solution are relatively simple and can be applied instead to a linear model for achieving accurate results.