Overdamped trap relaxation after an inertial boundary layer

For $ϵ=km/{\gamma }^2\ll 1$, momentum relaxes in ${\tau }_m=m/\gamma$ while the trap relaxes in ${\tau }_k=\gamma /k$. After the fast transient, the slow amplitude is $x_0+{\tau }_m{v}_0+O(ϵ)$. Neglecting the initial-velocity contribution additionally requires $|{\tau }_m{v}_0|\ll |x_0|$; small Reynolds number alone does not prove this condition.