4.I.4B

A damped pendulum is described by the equation

$\ddot{x}+2 k \dot{x}+\omega^{2} \sin x=0,$

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

*Typos? Please submit corrections to this page on GitHub.*