Repeat Problem 17 for the system in Figure 5.52, where the input is the displacement \(z\) and the outputs are the displacements \(x_{1}\) and \(x_{2}\).

Data From Problem 17:

The input is the force \(f\) and the outputs are the displacement \(x_{1}\) of the mass and the displacement \(x_{2}\) of the massless junction A.

a. Draw the necessary free-body diagrams and derive the differential equations of motion. Determine the number of degrees of freedom and the order of the system.

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

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

FIGURE 5.52 Problem 18. m 1x1 elle k A elle x2