Why is r > sqrt(2) the isolation region?

For displacement transmissibility, the curve crosses T = 1 at r = √2. Above that frequency ratio the mass moves less than the base, so motion is isolated rather than amplified.

Is more damping always better?

No. Damping is valuable near resonance, where it limits the peak, but at high frequency it transmits more motion through the damper path.

Vibration Isolation Transmissibility

SDOF base-excitation isolator: transmissibility T(r,ζ), resonance peak, phase lag, and the isolation region above r = √2.

This is the standard linear SDOF isolator. Real mounts add nonlinear stiffness, stroke limits, rubber hysteresis, multi-axis modes, and payload-dependent natural frequency.

Live graphs

About this model

A vibration isolator can be modeled as a single-degree-of-freedom mass-spring-damper system whose base moves harmonically. The displacement transmissibility T = X/Y compares absolute mass motion X to base motion Y and depends on frequency ratio r = ω/ω_n and damping ratio ζ. This simulator plots the standard base-excitation formula, animates the base and payload, and marks the isolation region where T < 1, which begins at r > √2 for displacement transmissibility. Damping is a tradeoff: it reduces the resonance peak near r = 1 but increases high-frequency leakage. The page omits nonlinear mounts, stroke limits, rubber hysteresis, multi-axis coupling, and payload-dependent natural-frequency shifts.

Who it's for: Machine dynamics, vibration control, mechanical design, and instrumentation mounting introductions.

Key terms

Transmissibility
Vibration isolation
Base excitation
Damping ratio
Frequency ratio

How it works

Single-degree-of-freedom vibration isolator under harmonic base excitation: compare mass motion to base motion and locate the isolation region above r = sqrt(2).

Key equations

T = X/Y = sqrt(1+(2ζr)^2) / sqrt((1-r²)^2+(2ζr)^2)

r = ω/ω_n; T < 1 for r > sqrt(2), but damping trades peak reduction for high-r leakage

Frequently asked questions

Why is r > sqrt(2) the isolation region?: For displacement transmissibility, the curve crosses T = 1 at r = √2. Above that frequency ratio the mass moves less than the base, so motion is isolated rather than amplified.
Is more damping always better?: No. Damping is valuable near resonance, where it limits the peak, but at high frequency it transmits more motion through the damper path.

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