Viscous damper, steady-state harmonic (sinusoidal) response

Steady-state sinusoidal force/velocity/displacement amplitudes of a pure viscous damper of known damping constant C at a given frequency f — either from a known displacement amplitude or from a known force amplitude.

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Damping constant, C10³ Ns/mFrequency, fHzDisplacement amplitude, X_max (case 1)10⁻³ mForce amplitude, F_max (case 2)N

Velocity amplitude from displacement, V (case 1)12.57 10⁻³ m/s

Force amplitude from displacement, F (case 1)376.99 N

Velocity amplitude from force, V (case 2)12.57 10⁻³ m/s

Displacement amplitude from force, X (case 2)2 10⁻³ m

Method & references

Steady-state harmonic response F=C·V, V=ω·X of a linear viscous damper, X(t)=Xmax·sin(ωt) / F(t)=Fmax·sin(ωt).

The computation is a literal port of the original client-side JavaScript from /calculators/response.htm. Results are verified equal to the original by an automated golden-master test. No formula has been re-derived or “improved”.

Viscous damper, steady-state harmonic (sinusoidal) response — Engineering ABC