particular chain. For example, a damped spring thermalizes on a
timescale of order $\tau = 1/\gamma$ where the damping ratio $\gamma
\equiv \omega_0(-\zeta \pm \sqrt{\zeta^2-1}$, the natural angular
-frequency $omega_0 \equiv \sqrt{k/m}$, $\zeta \equiv b/2\sqrt{km}$,
+frequency $\omega_0 \equiv \sqrt{k/m}$, $\zeta \equiv b/2\sqrt{km}$,
and $b$ sets the drag $F_b = -bv$. For our cantilevers $\tau$ is
on the order of milliseconds, which is longer than a timestep.
However, the approximation is still reasonable, because there is