Question: For the simple pendulum shown in Figure E3.20, the nonlinear equations of motion are given by k (t) + sin 0(t) + 0(1) = 0,

For the simple pendulum shown in Figure E3.20, the nonlinear equations of motion are given by k (t) + sin 0(t) + 0(1) = 0, L m where

k (t) + sin 0(t) + 0(1) = 0, L m where g is gravity, L is the length of the pendulum, m is the mass attached at the end of the pendulum (assume the rod is massless), and k is the coefficient of friction at the pivot point. (a) Linearize the equations of motion about the equi- librium condition 00 = 0. (b) Obtain a state variable representation of the system. The system output is the angle (t). Pivot point Massless rod L, length 0(t) m, mass FIGURE E3.20 Simple pendulum.

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