One of the important classes of targets for the future space-based gravitational wave observatory LISA is extreme mass ratio inspirals (EMRIs), where long and accurate waveform modeling is necessary for detection and characterization. When modeling the dynamics of an EMRI, several effects need to be included, such as the modifications caused by an external tidal field. The effects of such perturbations will generally break integrability at resonance, and can produce significant dephasing from an unperturbed system. In this paper, we use a Newtonian analogue of a Kerr black hole to study the effect of an external tidal field on the dynamics and the gravitational waveform. We have developed a numerical framework that takes advantage of the integrability of the background system to evolve it with a symplectic splitting integrator, and compute approximate gravitational waveforms to estimate the time scale over which the perturbation affects the dynamics. We find that different entry points into the resonance in phase-space can produce substantially different dynamics. Finally, by comparing this time scale with the inspiral time, we find tidal effects will need to be included when modeling EMRI gravitational waves when , where is the small mass ratio, and measures the strength of the external tidal field.