The paper presents a model for a parametrically excited nonlinear 1-DOF damped mass-spring system. An approximate analytical technique is used to obtain the general polynomial whose roots give the response of the system in frequency domain when the parametric excitation acts in the first parametric resonance region. All the details needed for the implementation of the method are given. The model is suitable for the prediction of the parametrically excited roll motion of
ships in longitudinal regular waves, thus some examples of application are shown to analyse the behaviour of two different hulls. The proposed approximate frequency domain analysis is shown to be able to disclose some nonlinear features of the ship response still not well known in the field of Naval Architecture.
