For the system shown in Figure 5.46, the input is the force (f) and the outputs are

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For the system shown in Figure 5.46, the input is the force \(f\) and the outputs are the displacements \(x_{1}\) and \(x_{2}\) of the masses.

a. Draw the necessary free-body diagrams and derive the differential equations of motion.

b. Write the differential equations of motion in the second-order matrix form.

c. Using the differential equations obtained in Part (a), determine the state-space representation.

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