motion of the simple pendulum: + sin 0 = Te ml Consider the nonlinear equations of Derive the equilibrium points for the system and determine the corresponding small-signal linear models. To do that, we should (a) derive the equilibrium points, (b) define the state variables, x, and (c) write the equation of motion in state-variable form x Ax+ Bu where u is the control input you define. (d) What are the eigenvalues of each linear model? (e) From the results you obtain in Part (d), discuss their stability. If there are multiple equilibrium points, then you have to derive the state-variable representations of small-signal linear models for each equilibrium point.