(Solved): "Referring to Examples 35 and 36, consider the inverted-pendulum system shown in Figure 334 ...

"Referring to Examples 3–5 and 3–6, consider the inverted-pendulum system shown in Figure 3–34. Assume that the mass of the inverted pendulum is m and is evenly distributed along the length of the rod. (The center of gravity of the pendulum is located at the center of the rod.)Assuming that u is small, derive mathematical models for the system in the forms of differential equations, transfer functions, and state-space equations"