(a) Determine the natural frequencies and mode shapes of the torsional system shown in Fig. 6.11 for \(k_{t 1}=k_{t 2}=k_{t 3}=k_{t}\) and \(J_{1}=J_{2}=J_{3}=J_{0}\).

(b) If a torque \(M_{t 3}(t)=\) \(M_{t 0} \cos \omega t\), with \(M_{t 0}=500 \mathrm{~N}-\mathrm{m}\) and \(\omega=100 \mathrm{rad} / \mathrm{s}\), acts on the generator \(\left(J_{3}\right)\), find the amplitude of each component. Assume \(M_{t 1}=M_{t 2}=0, k_{t}=100 \mathrm{~N}-\mathrm{m} / \mathrm{rad}\), and \(J_{0}=1 \mathrm{~kg}-\mathrm{m}^{2}\).

Figure 6.11:-

Transcribed Image Text:

M3 M12 -03 02 Mn K K1 Turbine (J2) Compressor (1) FIGURE 6.11 Torsional system. K3 Generator (J3)