Model the following dynamic systems in state variable form. Clearly define the energy storage devices and the corresponding state variables which define the energy in each device. Define the order of the system. Draw the simulation diagram for each system. 4. 5. 6. Ci(+) R R L R3 www C Vio (4) I R ww eb J. J L 0000 C = R = e. (t) Cz 70000 C62) ke Jz Wout(+) J Wout(t) Problem 3 (5 points) u(t) Figure 3: Problem 3: System simulation diagram. Consider the linear system represented by the simulation diagram shown in figure 3. 0(t) (a) (4 points) Find the ODE corresponding to the above simulation diagram (b) (1 points) If u(t) is an input torque, and (t) is the output angle (in radians), what is the system equivalent inertia, Jeq, and equivalent linear rotational damping coefficient, Beq?