Transmissibility Calculator
Transmissibility is the ratio of force transmitted to force applied: at r = 2 with ζ = 0.1, TR = 0.355862, so about 64 % of the force is isolated.
0.355861707107063
Full answer, then cut to fewer decimals (not rounded):
- 0.355861707107063
- 0.35586170710706
- 0.3558617071070
- 0.355861707107
- 0.35586170710
- 0.3558617071
- 0.355861707
- 0.35586170
- 0.3558617
- 0.355861
- 0.35586
- 0.3558
- 0.355
- 0.35
- 0.3
- Magnification factor X/(F₀/k)
- 0.330409
- Phase angle of response
- 172.405 °
- Isolation
- 64.414 % of the force is isolated
Step-by-step solution
- TR = √[1 + (2ζr)²] ÷ √[(1 − r²)² + (2ζr)²]
- = √[1 + 0.16] ÷ √[9 + 0.16]
- = 0.355862
Transmissibility Formula
TR = √[1 + (2ζr)²] ÷ √[(1 − r²)² + (2ζr)²]
r = ω/ωn frequency ratio, ζ damping ratio
Worked Example
A machine running at twice the natural frequency with ζ = 0.1:
- TR = √[1 + (2ζr)²] ÷ √[(1 − r²)² + (2ζr)²]
- = √[1 + 0.16] ÷ √[9 + 0.16]
- = 0.355862
Phase angle of response: 172.405 ° · Isolation: 64.414 % of the force is isolated
More Theory of Machines and Vibrations Calculators
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ΔE = I ω² Cs = m k² ω² Cs
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Example: ΔE = 5000 J at 600 rpm with Cs = 2 % and k = 0.5 m: Moment of inertia I = 63.3257 kg·m².
Frequently asked questions
At what frequency ratio does isolation start?
For r > √2, where TR < 1 whatever the damping. Below √2 the mount amplifies the force.
Does damping help vibration isolation?
Damping limits the peak at resonance but raises TR in the isolation region (r > √2).
Sources
Last reviewed: . Factors are stored exactly and computed with 50-digit decimal arithmetic. See how we verify conversion factors.
Cite this page
APA
Scientific Converters. (2026, October 15). Transmissibility Calculator. Retrieved October 25, 2026, from https://scientificconverters.com/calculators/transmissibility-calculator/
IEEE
Scientific Converters, "Transmissibility Calculator," scientificconverters.com. Accessed: Oct. 25, 2026. [Online]. Available: https://scientificconverters.com/calculators/transmissibility-calculator/