For the system shown in Figure 5.38, the input is the force \(f\) and the output is the displacement \(x\) of the mass.

a. Draw the necessary free-body diagram and derive the differential equation of motion.

b. Using the differential equation obtained in Part (a), determine the transfer function. Assume that initial conditions are \(x(0)=0\) and \(\dot{x}(0)=0\).

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

FIGURE 5.38 Problem 1. 0000 m 7x