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Resonant Frequency (Mechanical) Calculator

Work out resonant frequency (mechanical) instantly with clear inputs, formula shown and shareable results.

About Resonant Frequency (Mechanical) Calculator

A structure's natural frequency is (1/2pi) sqrt(k/m) - the frequency at which a small driving force builds a large response. A 60 kg mass on 15,000 N/m of stiffness resonates at 2.52 Hz, uncomfortably close to walking cadence, which is why floor and footbridge design targets keeping the first mode above about 5 Hz.

Formulas

Resonant frequency

f = (1 / 2 pi) sqrt(k / m)

Static deflection link

f is approximately 15.76 / sqrt(deflection in mm)

Worked example

With the default values below, Resonant Frequency (Mechanical) Calculator returns Natural Resonant Frequency of 2.5165. Change any input above and every figure here is recalculated in your browser.

Inputs used

Stiffness kminimum 0 N/m
15,000 N/m
Massminimum 0 kg
60 kg

Results

Natural Resonant Frequency
2.5165 Hz
Angular Frequency
15.811 rad/s
Period
0.39738 s
Static Deflection
0.039227 m

Step by step

  1. 1Values used
  2. 2Resonant frequency
  3. 3Static deflection link
  4. 4Natural Resonant Frequency= 2.5165 Hz
  5. 5Angular Frequency= 15.811 rad/s
  6. 6Period= 0.39738 s
  7. 7Static Deflection= 0.039227 m

Assumptions and limits

  • The result is derived only from the 2 inputs listed above. Anything not among them is not part of the calculation.
  • In particular, this calculator does not take inflation, tax, fees or charges or compounding frequency into account.
  • Figures are rounded for display to 6 decimal places, so totals built from several rounded parts can differ slightly from the unrounded arithmetic.

How these calculators are built and tested is described on the Methodology page. If a figure looks wrong, please report it.

Frequently Asked Questions

Why is resonance dangerous?

At resonance the response is limited only by damping, so a modest repeated force can build displacements large enough to fail the structure.

How do I shift a resonance away from a driving frequency?

Add stiffness to raise it or mass to lower it; frequency scales with the square root, so a 4x stiffness change only doubles it.

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