An optimally designed Houdaille damper is to be used to absorb the vibrations of a rotational system. The moment of inertia of the primary system is \(0.1 \mathrm{~kg} \cdot \mathrm{m}^{2}\) and the moment of inertia of the damper is to be is \(0.01 \mathrm{~kg} \cdot \mathrm{m}^{2}\).

(a) What is the optimum damping ratio?

(b) What is the steady-state amplitude of the primary system if \(\frac{M_{0}}{k}=0.002\) ?