Exact and Approximate Values of the Period for a "Truly Nonlinear" Oscillator: $\ddot{x} + x + x^{1/3} = 0$ (Advances in Applied Mathematics and Mechanics, 2018)
We investigate the mathematical properties of a "truly nonlinear" oscillatordifferential equation. In particular, using phase-space methods, it is shownthat all solutions are periodic and the fixed-point is a nonlinear center. We calculateboth exact and approximate analytical expressions for the period, where the exactsolution is given in terms of elliptic functions and the method of harmonic balanceis used to calculate the approximate formula.