Notes on a conservative nonlinear oscillator

Abstract

The amplitude–frequency relationship is an important mathematical property for a nonlinear oscillator. He’s amplitude–frequency formulation and the Max–Min approach are used to handle the conservative nonlinear oscillator x ̈ + ( 1 + x ̇ 2 ) x = 0 for the amplitude–frequency relationship. The obtained result is compared with those in the open literature, revealing the effectiveness of the used methods.