Does this result approve a machine foundation or isolation system?

No. It is a reference calculation for one documented linear force-excited degree of freedom. It does not apply an ISO acceptance criterion or include coupled modes,base compliance,soil impedance,transients or structural stress.

What happens at exact resonance with zero damping?

The ideal steady-state transfer denominator is zero. The calculator reports the singularity explicitly instead of displaying a finite response,NaN or Infinity.

Linear force-excited model — one degree of freedom

Rotating-Unbalance SDOF Force-Transmission Check

Calculate peak 1× excitation force,steady-state displacement and transmitted support force for one documented equivalent mass–spring–damper mode.

F₀=Uω²Peak amplitudesReference model — no acceptance decision

Peak-amplitude SDOF result

Excitation force F₀,peak

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Undamped natural frequency fₙ

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Frequency ratio r

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Displacement X,peak

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Force transmissibility T_F

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Transmitted support force F_T,peak

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Force reduction (negative = amplification)

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Implemented steady-state model

mẍ+cẋ+Kx=F₀cos(ωt)
ω=2πn/60 ; F₀=Uω²
ωₙ=√(K/m) ; r=ω/ωₙ ; ζ=c/(2mωₙ)
D=√[(1−r²)²+(2ζr)²]
X=(F₀/K)/D
T_F=√[1+(2ζr)²]/D ; F_T=F₀T_F

m is the combined participating mass in kg,K is the equivalent stiffness in N/m,U is converted from g·mm to kg·m by 10⁻⁶,n is rpm,ω and ωₙ are rad/s,X is the peak displacement amplitude in metres,and F₀ and F_T are peak force amplitudes in newtons. Force reduction is (1−T_F)×100%; a negative value explicitly means amplification.

Source and dimensional check

MIT OpenCourseWare,Rotating Imbalance derives the harmonic force components with amplitude meω². MIT OpenCourseWare,Vibration Isolation derives the force-excited SDOF response and transmitted-force ratio. Units check:F₀=(kg·m)/s²=N;F₀/K=N/(N/m)=m.

Interpretation limits

The result is not a balance tolerance,a vibration-severity value,a foundation design or a safe/unsafe verdict. Enter only equivalent mass,stiffness,damping and unbalance supported by project data. Total phase-coherent U means the vector-equivalent unbalance producing the modeled 1× force component; unrelated rotors or phases cannot simply be added as scalars. Peak amplitudes must not be compared directly with RMS or peak-to-peak limits.

Ideal undamped resonance

When ζ=0 and r=1,the steady-state transfer denominator is zero. The ideal linear model has no finite harmonic steady-state response. The calculator reports that singularity explicitly; real systems require measured/modelled damping and transient analysis near resonance.