How this calculator works
Viscous damping is proportional to velocity. Dividing its coefficient by the critical coefficient produces a dimensionless damping ratio. The plotted free response starts at unit displacement with zero velocity and uses natural time, so it works even when only the critical coefficient is known. It describes a linear single-degree-of-freedom oscillator without external forcing.
Formula
zeta = c/c_critical; c_critical = 2 sqrt(k m) = 2 m omega_n; omega_n = sqrt(k/m). The free response satisfies x'' + 2 zeta x' + x = 0 in natural time.
Worked example
With m = 1 kg, k = 4 N/m and c = 4 N s/m, critical damping is 4 N s/m and zeta = 1. A coefficient of 3 against a critical coefficient of 12 gives zeta = 0.25.
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Frequently asked questions
What do the ratio ranges mean?
Below one the response oscillates while decaying, one is critical damping, and above one is an overdamped response.
Are damping coefficient and spring stiffness interchangeable?
No. Damping uses N s/m and stiffness uses N/m. Their units differ even if their numeric values happen to match.
Does the chart include a driving force?
No. It shows free decay after release from rest, without a periodic or step force.