Summary: A recently developed analytical algorithm for generating the polyharmonic balance equations of a class of nonlinear differential equations has been used to perform a detailed four-component analysis of a single-degree-of-freedom ship roll model with cubic damping and quintic stiffness terms subject to a biased sinusoidal forcing function. The tradeoff between accuracy and complexity has then been systematically investigated across a range of input sinusoidal frequency, amplitude, and input bias, by investigating the effect of neglecting harmonic or model terms in the more detailed analysis and then comparing the results to independent solutions obtained through direct numerical integration of the governing equation.