It is well known in the marine hydrodynamics field that the radiated wave force is frequency dependent. However, much work in the nonlinear marine dynamical systems field has assumed frequency independence or a constant coefficients approximation. Assuming constant coefficients may be a reasonable approximation for single frequency steady state motion and even the transient response of a nonlinear system with a single frequency excitation but clearly not for multiple frequency excitation. In this work we will assess the effect of approximating the radiated wave force by constant coefficients versus the more accurate impulse response function modeling. We will apply these two types of hydrodynamic force modeling to calculate critical dynamics of ship rolling motion in regular and irregular waves. The critical dynamics are directly determined using a unique calculation method (Vishnubhotla, Falzarano, Vakakis, 2000). This method directly calculates motions on either the stable and unstable manifolds. Since the stable manifolds form the basin boundaries, the safe basin can be defined. Moreover, this method can be used as an alternative to the so-called Melnikov method by directly calculating the distance between the stable and unstable manifolds. This method is potentially more powerful than Melnikov methods since is it not dependent upon the so-called \"Melnikov trick\" which practically limits the Melnikov method to first order. This paper will contain results of constant coefficients (for various constant frequencies) versus impulse response function for regular wave excitation and various spectra. © Springer-Verlag Berlin Heidelberg 2009.