A turbine rotor of mass \(200 \mathrm{~kg}\) has an unbalanced mass of \(15 \mathrm{~kg}\). It is supported on a foundation which has an equivalent stiffness of \(5000 \mathrm{~N} / \mathrm{m}\) and a damping ratio of \(\zeta=0.05\). If the rotor is found to vibrate with a deflection of \(0.1 \mathrm{~m}\) at resonance, determine: (a) the radial location (eccentricity) of the unbalanced mass, (b) the additional mass to be added uniformly) to the rotor if the deflection of the rotor at resonance is to be reduced to \(0.05 \mathrm{~m}\), and (c) the peak deflection of the turbine when the frequency ratio \((r)\) varies.