On Almost Periodic Solutions for Undamped Systems with Almost Periodic Forcing

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Using the method of averaging, we give sufficient conditions for the existence of an almost periodic solution of an undamped oscillatory system with almost periodic forcing, and show that these can be applied to a Duffing equation with almost periodic forcing provided the nonlinear term is sufficiently small, and the natural frequency of the linear part of the system is included in the set of Fourier exponents of the forcing function.