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THE FEUTEX TOOLKIT

Damped Oscillator Forced Response

Find natural frequency, damping ratio and harmonic displacement amplitude.

Mechanical workspace● Runs in your browser
01 Your input
02 Your result
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Formulaωn=√(k/m); ζ=c/(2√km); X=F/√[(k−mω²)²+(cω)²].
Sources and model references

Worked example

Inputs

Mass
10 kg
Stiffness
1000 N/m
Viscous damping
20 N·s/m
Excitation angular frequency
5 rad/s
Harmonic force amplitude
10 N

Expected results

Undamped natural frequency
1.591549431 Hz
Damping ratio
0.1
Steady displacement amplitude
0.01321637201 m

Load the example in the workspace to reproduce these results. Display rounding does not change the underlying calculation.

How to use this tool

  1. Enter every input in the labeled units; use measured or independently specified properties.
  2. Check the stated model assumptions before calculating.
  3. Interpret the output as a model estimate and verify it independently for the intended application.

Try this example

{
  "mass": 10,
  "stiffness": 1000,
  "damping": 20,
  "omega": 5,
  "force": 10
}

Accuracy and scope

Linear single degree of freedom, viscous damping, steady harmonic response; transient response excluded. Educational engineering estimate only; not structural or safety certification, equipment selection, or operating recommendations.

Is my data uploaded?

This tool runs locally in your browser. Input and output are not sent to a processing server. Copy or download your result before leaving the page.