Damping Ratio
Damping Ratio
The damping ratio tells you whether a system oscillates, returns smoothly, or sluggishly — the single number that classifies its response.
The damping ratio is ζ = c/(2·√(k·m)). where c is the damping coefficient, k the stiffness and m the mass.
Inputs
c := 1500 N·s/m=1500 kg/s
k := 30000 N/m=30000 kg/s^2
m := 250 kg=250 kg
Compare actual damping to the critical value.
zeta := c/(2·sqrt(k·m))=0.27
Results
Below 1 the system is underdamped and oscillates; at 1 it is critically damped (fastest non-oscillating return); above 1 it is overdamped and slow. Cars aim for about 0.2–0.3.
Assumptions & limitations
- Single degree of freedom, viscous damping.
- Linear system.
- Constant coefficients.