Critical Damping Calculator

Your details

Mass of the oscillating body.
kg
Stiffness (spring constant) of the restoring element.
N/m
The actual damping coefficient of your system. Leave at the default to explore critical damping. Change it to compute the damping ratio and see whether your system is over-, under-, or critically damped.
N-s/m
Starting displacement from equilibrium, used only for the time-response chart. Does not affect the damping parameters.
m
The fraction of the initial displacement at which the response is considered "settled". 2 % is the conventional engineering definition.
Critical damping coefficient (cc)Underdamped (oscillates)
200N-s/m

Minimum damping that eliminates oscillation

Critical damping coefficient200.0000 N-s/m
Natural frequency (wn)10rad/s
Natural frequency (fn)1.5915Hz
Damping ratio (zeta)0.3163
Damped natural frequency (wd)9.4868rad/s
Settling time (ts)1.237s
Quality factor (Q)1.581
System typeUnderdamped
0.3163
Highly underdamped<0.5Underdamped0.5-0.9Critically damped0.9-1.1Overdamped1.1-2Highly overdamped2+

Underdamped - system will oscillate

  • Your system is underdamped (zeta = 0.316): it will oscillate before settling, with a damped frequency of 9.487 rad/s.
  • To eliminate oscillation, increase the damping coefficient to at least 200.0000 N-s/m.
  • The undamped natural frequency is 1.5915 Hz (10.0000 rad/s).
  • Estimated settling time within the 2% band: 1.237 s.

Next stepConsider increasing your damping coefficient or reducing mass/stiffness to reach critical damping and eliminate oscillation.

 = Powered by OnlyCalculators