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Dust settling is the vertical drift of solid particles toward a disk's midplane under gravity and drag force. In the strong-drag limit, a particle with aerodynamic stopping time $\tau$ settles through a linear vertical gravitational field at rate ${\Omega }_z^2\tau$.

Gas in hydrostatic balance has zero vertical velocity. A dust grain subject to linear drag with aerodynamic stopping time $\tau$ therefore obeysThis is a damped harmonic oscillator. For ${\Omega }_z\tau >1/2$, the motion is underdamped, with angular frequencyand envelope $e^{-t/(2\tau )}$. Critical damping occurs at ${\Omega }_z\tau =1/2$. For ${\Omega }_z\tau <1/2$, the motion is overdamped. In the strong-drag limit ${\Omega }_z\tau \ll 1$, a rapid transient on timescale $\tau$ leaves slow dust settling in an astrophysical disk at rate ${\Omega }_z^2\tau$; in the weak-drag limit the grain makes many damped vertical oscillations.