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Damping ratio

Damping removes energy from a vibration, for example as heat in a shock absorber. The damping ratio ζ\zeta compares the actual damping with the critical damping. If ζ<1\zeta < 1 the system oscillates with decaying amplitude (underdamped), if ζ=1\zeta = 1 it returns as fast as possible without oscillating (critical), and if ζ>1\zeta > 1 it returns even more slowly (overdamped).

ζ=c/cc\zeta = c/c_cdamping ratio
cc=2kmc_c = 2\sqrt{km}critical damping coefficient

Symbols

ζ\zetadamping ratio
ccdamping coefficientNs/m
ccc_ccritical damping coefficientNs/m

Example

m=4m = 4 kg, k=4000k = 4000 N/m, c=100c = 100 Ns/m:

cc=24000⋅4=400c_c = 2\sqrt{4000\cdot 4} = 400 Ns/m, so ζ=100/400=0.25\zeta = 100/400 = 0.25 (underdamped).

ζ=1\zeta = 1 is the boundary: the fastest return to rest without overshooting equilibrium.
Practise damping for free →

← Static deflection and frequency · Damped natural frequency →

Part of Machine Dynamics and Vibrations: Damping.