Critical Damping Requirement
Quickly calculate the critical damping coefficient and compare it to your actual damper to understand the resulting damping ratio.
Engineering estimate only—validate with lab testing or OEM specifications before commissioning equipment.
Examples
- 250 kg mass, 180,000 N/m stiffness, 1,500 N·s/m damping ⇒ Critical damping coefficient: 13,416.41 N·s/m; Actual ζ = 0.11
- 75 kg mass, 60,000 N/m stiffness, ζ target 0.35 ⇒ Required c: 1,484.92 N·s/m
FAQ
What if my damping is expressed in lb·s/in?
Convert imperial coefficients to N·s/m before entering them (multiply by 175.13) so the formula stays in SI units.
Can I use this for rotating equipment?
Yes—treat the equivalent mass and stiffness of the rotor-bearing system as the inputs and compare ratios to industry guidelines.
How do I interpret the damping ratio ζ?
ζ < 1 is underdamped (oscillatory), ζ = 1 is critically damped (fastest non-oscillatory response), and ζ > 1 is overdamped (slower but no overshoot).
Does nonlinear stiffness break the calculation?
The tool assumes linear stiffness; for strongly nonlinear systems, linearise around the operating point before entering the effective k value.
Additional Information
- Critical damping cₑ equals 2·√(k·m); ratios below 1 lead to oscillatory behaviour while ratios of 1 or higher eliminate overshoot.
- Enter stiffness in N/m—convert from kN/m by multiplying by 1,000 if needed.
- Target damping ratio lets you size new dampers even when the existing coefficient is unknown or being replaced.