A simple model for a ship rolling on waves* treats the waves as sinusoids. Using this mode...

A simple model for a ship rolling on waves* treats the waves as sinusoids. Using this model, it can be shown that a linear model for the roll angle θ is given by

where G denotes the mass center of the ship, IG is the ship’s mass moment of inertia, c is a rotational viscous damping constant coefficient, m is the mass of the ship, A is the wave amplitude, and k is the wavelength of the waves.

(a) What is the natural frequency of the system?

(b) Find the magnification factor for the system.

(c) Assuming that the damping is negligible (i.e., c ≈ 0), if the maximum amplitude of oscillation that the ship can undergo without capsizing is θmax = 1 rad, find the maximum A so that the crew remains safe.

Figure P9.65