Develop the linear model of a just a simple pendulum (vertically down) of length l and mass m with an ideal linear torsional spring k at the pivot joint of the pendulum b. draw the root locus of the system for k. (you may assume unity for all other parameters) c. describe the stability of the system in terms of the value k d. draw the block diagram of the system in terms of l e. draw the root locus of the system for the pendulum as you vary l (again, you may assume unity for all parameters)