A trailer of mass \(M\), connected to a wall through a spring of stiffness \(k\) and a damper of damping coefficient \(c\), slides on a frictionless surface, as shown in Fig. 5.49. A uniform rigid bar, pin-connected to the trailer, can oscillate about the hinge point, \(O\). Derive the equations of motion of the system under the applied forces \(F(t)\) and \(M_{t}(t)\) indicated in Fig. 5.49.

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F(t) x(t) Trailer, mass M M,(t) |0(1) Rigid bar, length I, mass m FIGURE 5.49 Trailer and rigid bar.