SHM Energy and Amplitude Calculator

Master simple harmonic motion with a powerful calculator for students engineers and researchers. Input mass stiffness or frequency and displacement. See amplitude energy velocity period and phase. Validate scenarios with units error checks and formulas for learning and labs. Works with spring constant or angular frequency. Calculates vmax amax potential kinetic energy and more.

Inputs
Provide any consistent set. Missing fields are inferred when possible.
Required if using stiffness to compute frequency.
Optional when angular frequency is known.
If omitted it may be inferred from mass and stiffness.
If omitted it may be inferred from total energy or vmax.
If omitted it may be inferred from A and stiffness or frequency.
vmax equals ωA.
Used for U K and instantaneous speed v(x).
Reset
Formulas and tips
  • Total energy E = ½ k A² = ½ m ω² A²
  • Potential energy U(x) = ½ k x²
  • Kinetic energy K(x) = E − U(x)
  • Speed at displacement v(x) = ω √(A² − x²) for |x| ≤ A
  • Period and frequency T = 2π/ω and f = ω/(2π)
  • Peaks vmax = ωA and amax = ω²A

Consistency: units must be coherent such as kg N m s J.

Inference: leave a field blank to let the tool infer it from other inputs.

Units reference
  • m: kilogram
  • k: newton per meter
  • ω: radian per second
  • A and x: meter
  • v: meter per second
  • E U K: joule
FAQs
Total energy equals one half k A squared. It also equals one half m omega squared A squared. Both forms are equivalent when k equals m omega squared.
You can use total energy with stiffness. Or total energy with mass and angular frequency. Or maximum speed with angular frequency. Any one of these sets is sufficient.
Yes. Angular frequency equals the square root of stiffness over mass. The tool uses this identity to infer values when possible.
An output is shown only when it follows from your inputs without contradiction. If the needed information is missing or inconsistent the value remains empty.
The model requires the magnitude of displacement to be no greater than amplitude. If it is larger the instantaneous speed is undefined and the tool raises an error.
Yes. It expects coherent SI units. For example kilogram newton per meter radian per second meter and joule. Keep your entries in the same system for correct results.
Period equals two pi over omega. Frequency equals omega divided by two pi. Both follow directly from the definition of angular frequency for harmonic motion.

Important Note: All the Calculators listed in this site are for educational purpose only and we do not guarentee the accuracy of results. Please do consult with other sources as well.