Abstract
In this paper, two kinds of frequency-amplitude formulation are used to solve the generalized conservative nonlinear equation in the form of for any arbitrary power of n and m. This equation is a general form of plasma physics equations and the Duffing equation. A frequency analysis is carried out and the relationship between the angular frequency and the initial amplitude is obtained in closed analytical form. This equation is analyzed in three cases: as a plasma physics equation, as a higher order Duffing equation and as an equation with irrational restoring force. Comparison with the exact integration method is also made, revealing that the present method leads to accurate solutions.