ζ = 1 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.

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