Harmonic balance method for solving a large-amplitude oscillation of a conservative system with inertia and static non-linearity

In this paper, an analytical approximate technique based on harmonic balance method (HBM) is presented to obtain the approximate frequencies and the corresponding periodic solutions of a conservative oscillator having inertia and static non-linearity. The results of the present paper are valid for small and large amplitudes of oscillation. In previous articles, the first and second approximations were determined for the same oscillator; but the results were not close to the exact result. On the contrary, the new results of this paper are very close to the exact result.