A rigid plate, of mass \(50 \mathrm{~kg}\), is hinged along an edge \((P)\) and is supported on a dashpot with \(c=177 \mathrm{~N}-\mathrm{s} / \mathrm{m}\) at the opposite edge \((Q)\), as shown in Fig. 3.66. A small fan of mass \(25 \mathrm{~kg}\) and rotating at \(750 \mathrm{rpm}\) is mounted on the plate through a spring with \(k=40 \mathrm{kN} / \mathrm{m}\). If the center of gravity of the fan is located at \(2.5 \mathrm{~mm}\) from its axis of rotation, find the steady-state motion of the edge \(Q\) and the force transmitted to the point \(S\).

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k 000 R S -15 cm- -45 cm- C.G. -60 cm- FIGURE 3.66 Motion of damper due to unbalance in fan.