Use a two degree-of-freedom model to derive the differential equations governing the motion of the system of Figure P7.96. A thin disk of mass moment of inertia \(I_{D}\) is attached to the end of the fixed-free beam. Use \(x\), the vertical displacement of the disk, and \(\theta\), the slope of the end of the beam, as generalized coordinates.

FIGURE P7.96 L E, I Fo sin cot 1X m, I