g Ball en Figure 3. Schematic representation of the system Do the following steps symbolically, do not substitute the actual numerical values until the very end. 2.1. Draw the free body diagram for the ball. Write the Newton's second law for the ball, obtain the nonlinear equation of motion of the system. 2.2. Linearize the equation and take the Laplace transform to obtain the transfer function X(s) 8(s) 2.3. So far, you have obtained the plant transfer function. This plant is controlled by a position- controlled servo motor as the actuator. Include the following transfer function of the servo motor to your model: 2 Ga(s) = 0.01s+1