Derive the equation of motion and find the steady-state solution of the system shown in Fig. 3.45 for rotational motion about the hinge \(O\) for the following data: \(k=5000 \mathrm{~N} / \mathrm{m}\), \(l=1 \mathrm{~m}, m=10 \mathrm{~kg}, M_{0}=100 \mathrm{~N}-\mathrm{m}, \omega=1000 \mathrm{rpm}\).

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Uniform rigid bar, mass m k 00000 F(t) = Fo sin cot M FIGURE 3.44 Spring-supported rigid bar subjected to harmonic force.