A shaft, having a stiffness of \(3.75 \mathrm{MN} / \mathrm{m}\), rotates at \(3600 \mathrm{rpm}\). A rotor, having a mass of \(60 \mathrm{~kg}\) and an eccentricity of 2000 microns, is mounted on the shaft. Determine (a) the steady-state whirl amplitude of the rotor and (b) the maximum whirl amplitude of the rotor during start-up and stopping conditions. Assume the damping ratio of the system as 0.05.