A turbine of mass moment of inertia of \(0.5 \mathrm{~kg}-\mathrm{m}^{2}\) is connected to an electric generator of mass moment of inertia of \(0.3 \mathrm{~kg}-\mathrm{m}^{2}\) by a hollow steel shaft of inner diameter inner diameter \(3 \mathrm{~cm}\), outer diameter \(5 \mathrm{~cm}\), and length \(0.5 \mathrm{~m}\) (similar to the system in Fig. 5.17(c)). If the turbine is suddenly stopped while delivering \(80 \mathrm{~kW}\) of power at a speed of \(6000 \mathrm{rpm}\), the transmitted torque drops to zero. Find the resulting angular displacements of the turbine and the generator. Assume damping to be negligible in the system.

Figure 5.17:-

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m1 X1(t) k m2 X2(t) k |x(1) m (a) X2(1) k(x2-x1) m2 Rotor 2 (b) FIGURE 5.17 Semidefinite systems. (turbine) Shaft (c) Rotor 1 (air blower)