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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. Keywords: Harmonic balance method, Non-linear oscillation, Large amplitude