Calculator · Dynamics & Control
Natural Frequency Calculator
Undamped natural frequency, critical damping and damping ratio of a single-degree-of-freedom mass–spring–damper system from its physical mass, damping and stiffness.
Physical parameters
Results
| Natural frequency ωₙ = √(k/m) | 5 rad/s |
|---|---|
| Natural frequency fₙ = ωₙ/2π | 0.7958 Hz |
| Natural period Tₙ | 1.257 s |
| Critical damping c_c = 2√(km) | 20 N·s/m |
| Damping ratio ζ = c/c_c | 0.3 |
| Damping regime | underdamped |
| Damped natural frequency ω_d | 4.77 rad/s |
Technical reference
ωₙ = √(k/m)
fₙ = ωₙ / (2π)
- m
- lumped mass[kg]
- k
- spring stiffness[N/m]
- ωₙ
- undamped natural frequency[rad/s]
- fₙ
- undamped natural frequency[Hz]
This calculator focuses on the undamped ωₙ and fₙ derived from m and k; when c is supplied, it also reports critical damping, ζ and the damping regime, and ω_d only when the system is underdamped (ζ < 1). For additional SDOF quantities — damped period, logarithmic decrement, quality factor, compliance, poles and the X(s)/F(s) transfer function — see the Mass–Spring–Damper Calculator.
Assumptions
- Single degree of freedom, lumped mass, linear spring and linear viscous damper.
- Constant parameters; no Coulomb friction, backlash or geometric nonlinearity.
- ωₙ is the UNDAMPED natural frequency. The frequency actually observed in a damped free decay is ω_d = ωₙ√(1 − ζ²), reported separately above.
Continue in the Lab
Open these exact parameters in the Vibrations Lab to see the free decay, forced response, resonance and transmissibility.