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Engineering · Vibration & Rotating Systems

Two-Mass Two-Spring Natural Frequency Calculator

Calculate the two undamped natural frequencies of a serial two-mass system with one spring to ground and one coupling spring.

Engineering · Vibration & Rotating Systems

Enter the engineering model

Explicit properties, geometry, units and assumptions
  1. 1EnterProvide the known values
  2. 2CalculateResults update automatically
  3. 3VerifyReview the details and units
Try an example
Visual modelSchematic · not to scale
Vibration & Rotating Systems: twoMass visual explanationA simplified diagram showing the relationship represented by the selected calculator mode. It is explanatory and not a fabrication, safety or scale drawing.two coupled masses → two natural frequencies
The diagram explains the selected relationship only. Dimensions, symbols and proportions are illustrative; use the entered values and stated assumptions for the calculation.

Keep every unit basis, sign convention, property source and idealization consistent. Values stay in this browser.

Engineering calculation result

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Enter valid values to see the result.

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Understand the dynamic model

What this calculator is for

Calculate the two undamped natural frequencies of a serial two-mass system with one spring to ground and one coupling spring. It exists to make the selected ideal model, its inputs, and its limits visible before the result is used elsewhere.

1Match the physical system to the displayed mass, stiffness, damping and support topology.
2Use one consistent force, length, mass and time basis.
3Compare the intermediate frequency or ratio outputs before interpreting amplitude.

Visual explanation

The tailored schematic separates inertia, elastic restraint, damping or excitation so the governing relationship can be read as a physical model rather than an unexplained formula.

The governing relationship

det(K−ω²M)=0 with M=diag(m₁,m₂) and K=[[k₁+k₂,−k₂],[−k₂,k₂]].

Keep the boundary visible

Undamped two-degree lumped model only. Mode shapes are relative, and real constraints, distributed mass and damping are excluded.

Quick guide

How to use this calculator

  1. Choose the analysis mode that matches the physical model before entering values.
  2. Enter properties, geometry, loads, states and coefficients from one consistent unit and sign convention.
  3. Use the intermediate outputs to audit the relationship, then retain the stated idealization before applying it.

Calculation method

Transparent engineering model

det(K−ω²M)=0 with M=diag(m₁,m₂) and K=[[k₁+k₂,−k₂],[−k₂,k₂]].

The calculator evaluates only the declared relationship and preserves visitor-entered assumptions rather than selecting materials, factors, components or standards.

Worked example

Worked example

Two equal 10 kg masses with k₁=k₂=1,000 N/m produce two distinct coupled natural frequencies.

det(K−ω²M)=0 with M=diag(m₁,m₂) and K=[[k₁+k₂,−k₂],[−k₂,k₂]].

Supported inputs

Precision and limits

Analysis, not approval

Undamped two-degree lumped model only. Mode shapes are relative, and real constraints, distributed mass and damping are excluded.

Standards and properties

Material properties, allowable values, load combinations, safety factors, correlations, manufacturer data, codes and jurisdictional requirements are not supplied automatically.

Units and precision

Use one consistent unit basis. Results retain working precision but cannot be more accurate than the entered measurements and properties.

Privacy

Entered engineering values and results stay in this browser and are not sent to analytics or third parties.