For the simple pendulum shown in Figure E3.20, the nonlinear equations of motion are given by
where g is gravity, L is the length of the pendulum, m is the mass attached at the end of the pendulum (we assume the rod is massless), and k is the coefficient of friction at the pivot point.
(a) Linearize the equations of motion about the equilibrium condition θ = 0°,
(b) Obtain a state variable representation of the system. The system output is the angle θ.
