Damped pendulum
= Damped pendulum
{title2=$\ddot\theta+c\dot\theta+\sin\theta=0$}
In units where the small-amplitude natural frequency is one, linear velocity drag gives $\ddot\theta+c\dot\theta+\sin\theta=0$ with $c>0$. The even multiples of $\pi$ are attracting equilibria; the odd multiples are <saddle equilibria>. Small displacements obey a <damped harmonic oscillator>; the <energy dissipation of a damped pendulum> governs the global <phase portrait>.