The equation of motion for the free oscillations of a pendulum subject to quadratic damping is [

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The equation of motion for the free oscillations of a pendulum subject to quadratic damping is

\[ \ddot{\theta}+2 \zeta \dot{\theta}^{2}+\sin \theta=0 \]

(a) Determine an exact equation defining the state plane.

(b) Determine the equilibrium points and their type.

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