(Solved): B-3-5. Referring to Examples \( 3-5 \) and \( 3-6 \), consider the inverted-pendulum system shown i ...

B-3-5. 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 \( \theta \) is small, derive mathematical models for the system in the forms of differential equations, transfer functions, and state-space equations. Figure 3-34 Inverted-pendulum system.