Antidamping
= Antidamping
{title2=$\ddot x+2\lambda\dot x+\omega_0^2x=0,\quad\lambda<0$}
<antidamping> is a velocity-proportional term that supplies rather than removes mechanical <energy>. For the displayed <damped harmonic oscillator> with negative damping coefficient, $d[(\dot x^2+\omega_0^2x^2)/2]/dt=-2\lambda\dot x^2\geq0$. <causality> of a driven solution and its long-time stability are different properties.