When studying the dynamics of ice-structure interaction, hydrodynamic effects are often ignored to simplify the model. One of the challenges associated with the introduction of the hydrodynamic forces is that those introduce frequency dependent added mass and damping into the system. In order to include these two components in a time domain model with a non-linear contact model, a convolution integral is needed to compute the response of the body. Computing the convolution integral is computationally intensive and as such undesired. In this paper a methodology is presented which allows the time domain response of a floating ice block (a rigid body) to be computed, including the effects of hydrodynamics, without having to resort to using a convolution integral. This is done by approximating the complex frequency response of the floating body with that of an equivalent dynamical system. By choosing a replacement system whose time domain representation can be readily solved with an ODE solver, the time domain response of the original floating ice block can be obtained without having to evaluate a convolution integral. Ultimately, a replacement system with only three degrees of freedom is needed to compute the time domain response of the floating block of ice with an error in the heave motion of about 0.1%.