Periodic Solution of a Cubic-Quintic Duffing Oscillator

The cubic-quintic Duffing oscillator covers important applications in physics and engineering.A simplification of recent methods,for large amplitudes,is proposed.An asymptotic solution is found and utilized to find a simple uniformly valid expression for the period of a cubic-quintic Duffing oscillator.It is shown that for 0A∞,energy stored in the fundamental harmonic exceeds 80%