The input to the translational mechanical system shown in the following diagram is the displacement \(x_{3}(t)\) of the right end of the spring \(k_{1}\). The absolute displacements of \(m_{1}\) and \(m_{2}\) are \(x_{1}\) and \(x_{2}\), respectively. The forces exerted by the springs are zero when \(x_{1}=x_{2}=x_{3}=0\).

(a) Draw the free-body diagrams of the system.

(b) Obtain the system dynamic equations of motion.

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k ele ele k X1 X2 m XXXX-b (1) Ex k 000 m CO Translational Mechanical System