Abstract
In this paper we use the method of derivative expansion of multiple scales of singular perturbations, and we have solve the forced vibration equation of a particle attached to a nonlinear spring under the influence of slight viscous damping. The problem is of the fourth order nonlinearity. The four cases discussed are: the soft excitation of non-resonance, the hard excitation of non-resonance, the soft excitation of resonance, the hard excitation of resonance.
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