Damping Ratio Calculator

Your details

Choose whichever method matches the values you have. All three give the same damping ratio.
Mass of the oscillating body in kilograms.
kg
Stiffness of the spring or restoring element in newtons per metre.
N/m
Viscous damping coefficient in newton-seconds per metre. Dashpot constant for linear dampers.
N·s/m
Damping ratioUnderdamped
0.2

Dimensionless ratio; < 1 underdamped, = 1 critically damped, > 1 overdamped

Critical damping coefficient200N·s/m
Natural frequency (undamped)10rad/s
Natural frequency (damped)9.798rad/s
Natural frequency (Hz)1.5915Hz
Logarithmic decrement1.2825
Quality factor (Q)2.5
0.2 zeta
Lightly damped<0.2Underdamped0.2-0.7Near critical0.7-1Overdamped1+

Damping ratio is 0.2000 (20.0% of critical): the system is underdamped and will oscillate with decaying amplitude.

  • Quality factor Q = 2.50: a lower Q means faster energy loss per cycle.
  • Logarithmic decrement = 1.2825: amplitude drops by a factor of e^1.28 each oscillation cycle.
  • Moderate damping: typical for well-designed automotive suspensions, vibration isolators and structural systems.
  • Undamped natural frequency: 10.000 rad/s; damped natural frequency: 9.798 rad/s.

Next stepConsider increasing the damping coefficient to move into the 0.5 to 0.8 range for faster settling without large overshoot.

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