Free · Physics models
Viscous Oscillator Damping Ratio
Calculate damping ratio from spring stiffness, natural angular frequency or the critical damping coefficient.
- Formula & worked example
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Calculator inputs
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How to use this calculator
- Enter the known values in the units shown. Results update as you type.
- Where results are editable, change one to solve backwards. Lock a value to hold it fixed.
- Use the worked example to check the method. Reset restores the starting fields.
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Formula and method
Damping ratio = 0.50000000. The worked example lists its inputs and unit conventions.
ζ = c/(2√(mk)) = c/(2mωn) = c/ccrit.
Worked example
Enter these known values and leave the other values blank.
- Method
- 0
- Viscous damping coefficient (selected force/length unit × s)
- 10 N/m ⋅ s ·s
- Suspended mass
- 1 kg
- Spring constant
- 100 N/m
- Damping ratio
- 0.5
Assumptions and limitations
- A linear single-degree-of-freedom viscous oscillator is assumed. Damping coefficients have units force×time/length: multiply the selected force/length unit by one second, as shown by the added s suffix. Mass and stiffness must be positive. ζ<1 is underdamped, ζ=1 critically damped and ζ>1 overdamped. The retained positive-damping branch excludes c=0.
- Clear an unknown quantity and lock known quantities to solve a supported inverse. Supply compatible values for the selected model.
Common questions
What branch does this use?
A linear single-degree-of-freedom viscous oscillator is assumed. Damping coefficients have units force×time/length: multiply the selected force/length unit by one second, as shown by the added s suffix. Mass and stiffness must be positive. ζ<1 is underdamped, ζ=1 critically damped and ζ>1 overdamped. The retained positive-damping branch excludes c=0.
Can I solve an inverse?
Yes. Editable numeric fields retain the captured inverses, subject to the selected physical branch and known quantities.
References
A linear single-degree-of-freedom viscous oscillator is assumed. Damping coefficients have units force×time/length: multiply the selected force/length unit by one second, as shown by the added s suffix. Mass and stiffness must be positive. ζ<1 is underdamped, ζ=1 critically damped and ζ>1 overdamped. The retained positive-damping branch excludes c=0.