A turbine rotor is mounted on a stepped shaft that is fixed at both ends as shown in Fig. 05. The torsional stiffnesses of the two segments of the shaft are given by kt1 = 3,000 N-m/rad and kt2 = 4000 N-m/rad. The turbine generates a harmonic torque given by M(t) = Mo cos ωt about the shaft axis with Mo = 200 N-m and ω = 500 rad/s. The mass moment of inertia of the rotor about the shaft axis is Jo = 0.05 kg-m ² . Assuming the equivalent torsional damping constant of the system as ct = 2.5 N-m-s/rad, determine the steady-state response of the rotor, θ(t).

ke MO) = M, cos at Turbine rotor, Jo