4.5 Article

Highly Accurate Analytical Approximate Solutions to Mixed-Parity Duffing Equation

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Summary: This study provides closed-form exact solutions for periodic motions of a nonlinear oscillator with a quadratic mixed-parity restoring force, characterised by two real parameters. Two families of exact solutions in terms of Jacobi elliptic functions are obtained, and the periods are given in terms of the complete elliptic integral of the first kind. The behavior of these periods as a function of the initial amplitude is analyzed and exact solutions for certain parameter values are plotted.

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