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