Consider the system shown in Figure 5.69, in which the motion of the rod is small angular rotation. When \(\theta=0\), the springs are at their free lengths.

a. Determine the mass moment of inertia of the rod about point O. Assume that \(a>b\).

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

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FIGURE 5.69 Problem 11. 10000 M k elle