The conservative Helmholtz-Duffing oscillator is analyzed by means of three analytical techniques. The max-min, second-order of\nthe Hamiltonian, and the global error minimization approaches are applied to achieve natural frequencies. The obtained results\nare compared with the homotopy perturbation method and numerical solutions. The results show that second-order of the global\nerror minimization method is very accurate, so it can be widely applicable in engineering problems.
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