| Scenario | Given | Result |
|---|---|---|
| Ratio + frequency | m=10 kg, ζ=0.05, fn=2.0 Hz | c = 2ζmωn = 2×0.05×10×(2π×2) ≈ 12.566 N·s/m |
| Ratio + stiffness | m=12 kg, k=18000 N/m, ζ=0.08 | ωn=√(k/m)≈38.729; c≈74.360 N·s/m |
| Log decrement | m=8 kg, δ=0.35, Td=0.42 s | ζ≈0.0556; ωn≈15.009; c≈13.342 N·s/m |
- Pick a method that matches your available measurements.
- Enter values using consistent units for mass and stiffness.
- If entering frequency in Hz, keep the unit selector on Hz.
- Press Calculate to see results above the form.
- Use Download CSV or Download PDF for documentation.
- Review “Response type” to confirm under, critical, or over damping.
1) What the damping coefficient represents
In a viscously damped oscillator, the damping coefficient c links velocity to resisting force: Fd = c·v. Its SI unit is N·s/m (equivalently kg/s). Higher c means faster energy loss, less ringing, and smaller overshoot after a disturbance.
2) How c relates to mass, stiffness, and frequency
For a single degree of freedom model, c is often computed from c = 2ζmωn. Natural frequency follows ωn=√(k/m). If you only know frequency in Hz, convert with ωn=2πf. The calculator also reports b=c/(2m), a useful decay rate in 1/s.
3) Typical damping ratio ranges
Damping ratio ζ is dimensionless and helps classify response. Many lightly damped structures fall around ζ≈0.01–0.05. Rubber-isolated mounts and some machinery can sit near ζ≈0.05–0.20. ζ=1 is critical damping; ζ>1 is overdamped, usually with no oscillation.
4) Critical damping as a useful benchmark
Critical damping coefficient is cc=2mωn. Your computed c can be compared via ζ=c/cc. In control and vibration work, a common settling-time estimate is ts≈4/(ζωn) for a 2% band, which shows how strongly ζ influences response speed.
5) Using decay data and logarithmic decrement
When you measure peak decay, logarithmic decrement δ=ln(x1/x2) gives ζ through ζ = δ/√(4π²+δ²). If you measure amplitudes A1 and A2 separated by Δt, the envelope relation yields ζ=ln(A1/A2)/(ωnΔt). For underdamped motion, percent overshoot is often approximated by e−πζ/√(1−ζ²)×100%.
6) Quality factor and resonance sharpness
In many resonance tests, Q≈1/(2ζ). A higher Q means a sharper resonance peak and slower decay. For example, ζ=0.02 gives Q≈25, while ζ=0.10 gives Q≈5. This tool reports Q from the computed ζ for quick checks.
7) Reporting results with consistent units
Use kg for mass, N/m for stiffness, seconds for time, and Hz or rad/s for frequency. Keep amplitudes in any consistent unit when using decay methods. After calculating, export CSV for spreadsheets or PDF for documentation, then store the inputs alongside outputs for traceability and repeatable reviews. Round results to match your measurement precision.
1) What unit does the damping coefficient use?
The standard SI unit is N·s/m, which is equivalent to kg/s. It represents the force produced per unit velocity in a viscous damper.
2) What is the difference between c and ζ?
c is an absolute damping level in N·s/m, while ζ is a dimensionless ratio that compares c to the critical damping value cc. ζ helps classify response behavior.
3) When should I choose the stiffness method?
Use the stiffness method when you know m, k, and ζ. It estimates ωn from √(k/m), which is convenient for spring–mass models and many vibration setups.
4) Can I enter frequency in Hz?
Yes. Select the Hz option and enter f. The calculator converts it to ωn=2πf internally, then computes c with c=2ζmωn.
5) Why does the tool show “underdamped” or “overdamped”?
The response type is determined by ζ. If ζ<1, motion oscillates with a decaying envelope. If ζ=1, it returns fastest without oscillation. If ζ>1, it returns slowly without oscillation.
6) What if I only have two amplitudes over time?
Use the amplitude decay method with A1, A2, and Δt, plus m and k. It estimates ζ from the exponential decay envelope and then calculates c from ζ, m, and ωn.