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Mass Spring Oscillation Calculator

Work out mass spring oscillation instantly with clear inputs, formula shown and shareable results.

About Mass Spring Oscillation Calculator

A mass on a spring oscillates at omega = sqrt(k/m), so a stiffer spring or a lighter mass raises the frequency. 0.5 kg on a 200 N/m spring gives 3.18 Hz. Gravity does not affect the frequency at all - it only shifts the equilibrium point down by mg/k, which is the static deflection shown here.

Formulas

Angular frequency

omega = sqrt(k / m)

Period

T = 2 pi sqrt(m / k)

Worked example

With the default values below, Mass Spring Oscillation Calculator returns Period of 0.3142. Change any input above and every figure here is recalculated in your browser.

Inputs used

Oscillating massminimum 0 kg
0.5 kg
Spring constant kminimum 0 N/m
200 N/m

Results

Period
0.3142 s
Natural Frequency
3.1831 Hz
Angular Frequency
20.0000 rad/s
Static Deflection Under Gravity
0.02452 m

Step by step

  1. 1Values used
  2. 2Angular frequency
  3. 3Period
  4. 4Period= 0.3142 s
  5. 5Natural Frequency= 3.1831 Hz
  6. 6Angular Frequency= 20.0000 rad/s
  7. 7Static Deflection Under Gravity= 0.02452 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 5 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

Does hanging the spring vertically change the period?

No. Gravity moves the rest position but the restoring force about that new position is still kx, so the frequency is unchanged.

How do I stiffen a system without changing mass?

Springs in parallel add their constants; springs in series reduce the effective constant. Doubling k raises frequency by only 41%.

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