Repeat Problem 7 for the system shown in Figure 5.68. When \(\theta=0\) and \(f=0\), the springs are at their free lengths.

Data From Problem 7:

a. Draw the necessary free-body diagram and derive the differential equation of motion for small angles \(\theta\).

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

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

FIGURE 5.68 Problem 8. 0 C M, L 13 elle