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We analyze the dynamics of the forced singularly perturbed differentialequation of Duffing's type. We explain the appearance of the large frequencynonlinear oscillations of the solutions. It is shown that the frequency can becontrolled by a small parameter at the highest derivative. We give somegeneralizations of results obtained recently by B.S. Wu, W.P. Sun and C.W. Lim,Analytical approximations to the double-well Duffing oscillator in largeamplitude oscillations, Journal of Sound and Vibration, Volume 307, Issues 3-5,(2007), pp. 953-960. The new method for an analysis of the nonlinearoscillations which is based on the dynamic change of coordinates is proposed.

Frequency control of singularly perturbed forced Duffing's oscillator