Math 2.0

Mechanics of particles and systems Linear vibrations Concept

Parametric oscillator

Builds on Harmonic oscillatorFloquet theory

Summary

A parametric oscillator is a harmonic oscillator whose parameters, such as its stiffness or its damping, change in time, usually periodically. The energy is pumped in by varying a parameter, not by a direct external force. When the parameter varies at about twice the natural frequency, small oscillations grow exponentially; this is parametric resonance. Periodic coefficients make Floquet theory the main tool, and the Mathieu equation is the standard model.

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Complex numbers, object, no evidence levelComplex numbersobjectDifferential equation, concept, no evidence levelDifferential equationconceptFloquet theory, concept, no evidence levelFloquet theoryconceptFunction, concept, no evidence levelFunctionconceptInterval, concept, no evidence levelIntervalconceptEuler's formula, statement, no evidence levelEuler's formulastatementOrdinary differential equation, definition, no evidence levelOrdinary differential…definitionOrder of a differential equation, definition, no evidence levelOrder of a differenti…definitionLinear differential equation of order n, definition, no evidence levelLinear differential e…definitionHomogeneous linear equation, definition, no evidence levelHomogeneous linear eq…definitionLinear equation with constant coefficients, definition, no evidence levelLinear equation with …definitionSuperposition principle, statement, no evidence levelSuperposition princip…statementCharacteristic equation, definition, no evidence levelCharacteristic equati…definitionSolution space of a homogeneous linear equation has dimension n, statement, no evidence levelSolution space of a h…statementFundamental system of solutions, definition, no evidence levelFundamental system of…definitionSolutions for distinct real roots, statement, no evidence levelSolutions for distinc…statementSolutions for repeated roots, statement, no evidence levelSolutions for repeate…statementSolutions for complex conjugate roots, statement, no evidence levelSolutions for complex…statementHarmonic oscillator, example, no evidence levelHarmonic oscillatorexampleParametric oscillator, concept, no evidence levelParametric oscillatorconcept
Each page uses the pages above it. The colour of the bar on a box shows how strong the evidence is, and the box also gives it as text. The list has the same pages.
  • no evidence level
  1. Complex numbers object
  2. Differential equation concept
  3. Floquet theory concept
  4. Function concept
  5. Interval concept
  6. Euler's formula statement
  7. Ordinary differential equation definition
  8. Order of a differential equation definition
  9. Linear differential equation of order n definition
  10. Homogeneous linear equation definition
  11. Linear equation with constant coefficients definition
  12. Superposition principle statement
  13. Characteristic equation definition
  14. Solution space of a homogeneous linear equation has dimension n statement
  15. Fundamental system of solutions definition
  16. Solutions for distinct real roots statement
  17. Solutions for repeated roots statement
  18. Solutions for complex conjugate roots statement
  19. Harmonic oscillator example
  20. Parametric oscillator concept

Where this leads

1 page builds on this one.

Further reading

  1. Web https://en.wikipedia.org/wiki/Parametric_oscillator
About this page
TagHF4K06Q6XX
URIm2://HF4K06Q6XX
Kindconcept
WritingW0 stub
MSC70J40, 34C25, 70K28
UsesHarmonic oscillator, Floquet theory
Same as
Changed3 November 2026

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