Dynamics | Part IA, 2008

A damped pendulum is described by the equation

x¨+2kx˙+ω2sinx=0,\ddot{x}+2 k \dot{x}+\omega^{2} \sin x=0,

where kk and ω\omega are real positive constants. Determine the location of all the equilibrium points of the system. Classify the equilibrium points in the two cases k>ωk>\omega and k<ωk<\omega.

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