1. Develop a mathematical model of the system shown in Figure 1. 2. Give the signal flow graph of the system. P M Figure 1. An inverted pendulum on a cart Where the mass of the cart is M and the mass of the bob at the end of the pendulum is m. The length of the pendulum rod is I. The angular position of the pendulum rod with respect to the vertical is 0, where 0 is positive to the right. f is the force applied to keep the pendulum bar at the desired position.

1. Develop a mathematical model of the system shown in Figure 1. 2. Give the signal flow graph of the system. P M Figure 1. An inverted pendulum on a cart Where the mass of the cart is M and the mass of the bob at the end of the pendulum is m. The length of the pendulum rod is I. The angular position of the pendulum rod with respect to the vertical is 0, where 0 is positive to the right. f is the force applied to keep the pendulum bar at the desired position.