A steel shaft of diameter \(2.5 \mathrm{~cm}\) and length \(1 \mathrm{~m}\) is supported at the two ends in bearings. It carries a turbine disc, of mass \(20 \mathrm{~kg}\) and eccentricity \(0.005 \mathrm{~m}\), at the middle and operates at \(6000 \mathrm{rpm}\). The damping in the system is equivalent to viscous damping with \(\zeta=0.01\). Determine the whirl amplitude of the disc at (a) operating speed, (b) critical speed, and (c) 1.5 times the critical speed.