ζ = 1 is critical damping

What is critical damping?

When the damping ratio hits 1, the system returns to rest as fast as possible without overshoot — less damps and it rings; more and it crawls.

Why it works

For mẍ + cẋ + kx = 0, ζ = c/(2√(km)). Critical damping is the boundary between oscillatory and exponential return.

Do it exactly

Estimate with the rule, then check it against the calculator that models it properly.

Open Mass-Spring-Damper →

More in Physics

• Hohmann is the cheapest transfer — until the ratio passes about 12Two burns on opposite sides of an ellipse is the minimum-energy route between circular orbits, a…
• A narrower gap spreads light more, not lessDiffraction angle goes as wavelength over aperture, so halving the opening doubles the spread — …
• Geostationary runs on the sidereal day, not the 24-hour oneThe altitude falls straight out of the period: match Earth’s rotation and the orbit radius is fi…
• The peak wavelength is about 2,900 divided by the temperatureA hot object shines brightest at a wavelength, in micrometres, of about 2,900 divided by its tem…

Browse the full Rulebook →