The mathematical treatment of the dynamics of a classical system when the latter is subjected to a time-dependent force is usually straightforward when the amplitude and the frequency of the external impetus are reasonably small. In such cases, standard perturbation treatments are available in the literature. However, when either (or both) the amplitude or (and) the frequency is (are) very large, the situation is much more complex. Ironically though, when the frequency is extremely large and the analysis may appear hopelessly complicated, a timescale separation emerges that makes the calculation much simpler.