Analysis & loading · Seismic & dynamic

Dynamic amplification (SDOF, harmonic) calculator

Dynamic amplification and force transmissibility for a damped single-degree-of-freedom system.

Standard: Single-degree-of-freedom response

Inputs in the worked example

The live calculator starts with these values; change any of them and every result, check and diagram updates instantly.

Diagram for the worked example

Natural frequency = SQRT(5000/2)/(2*PI()) = 7.9577 Hz
Frequency ratio = 6/7.9577 = 0.75398
DAF = 1/√((1 − r²)² + (2ζr)²) = 1/SQRT((1-0.75398^2)^2+(2*0.05*0.75398)^2) = 2.2829
Amplitude F0 DAF/k = 3*2.2829/5000*1000 = 1.3697 mm
Transmissibility = SQRT(1+(2*0.05*0.75398)^2)*2.2829 = 2.2893

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For preliminary design and education. Check every result against the current standard and your own engineering judgement before use.