In many derivations of ship-motion equations the result appears as a second-order linear differential equation with a sinusoidal driving force and frequency-dependent coefficients. The further assumption of linearity of the system with respect to any driving function is made. Thus the response to any function can be found by decomposing the forcing function into its frequency, components, using the given equation to find the response to each and summing the result.
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Leo J. Tick (1959) studied this question.