The homogeneity and additivity properties together are called the superposition principle. A linear function is one that satisfies the properties of superposition. It is defined as

This principle has many applications in physics and engineering because many physical systems can be modeled as linear systems. For example, a beam can be modeled as a linear system where the input stimulus is the load on the beam and the output response is the deflection of the beam. The importance of linear systems is that they are easier to analyze mathematically; there is a large body of mathematical techniques, frequency domain linear transform methods such as Fourier, Laplace transforms, and linear operator theory, that are applicable. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behaviour.

The superposition principle applies to *any* linear system, including algebraic equations, linear differential equations, and systems of equations of those forms. The stimuli and responses could be numbers, functions, vectors, vector fields, time-varying signals, or any other object that satisfies certain axioms. Note that when vectors or vector fields are involved, a superposition is interpreted as a vector sum.

By writing a very general stimulus (in a linear system) as the superposition of stimuli of a specific, simple form, often the response becomes easier to compute.

For example, in Fourier analysis, the stimulus is written as the superposition of infinitely many sinusoids. Due to the superposition principle, each of these sinusoids can be analyzed separately, and its individual response can be computed. (The response is itself a sinusoid, with the same frequency as the stimulus, but generally a different amplitude and phase.) According to the superposition principle, the response to the original stimulus is the sum (or integral) of all the individual sinusoidal responses.

As another common example, in Green's function analysis, the stimulus is written as the superposition of infinitely many impulse functions, and the response is then a superposition of impulse responses.

Fourier analysis is particularly common for waves. For example, in electromagnetic theory, ordinary light is described as a superposition of plane waves (waves of fixed frequency, polarization, and direction). As long as the superposition principle holds (which is often but not always; see nonlinear optics), the behavior of any light wave can be understood as a superposition of the behavior of these simpler plane waves.

This page was last edited on 13 May 2018, at 02:59 (UTC).

Reference: https://en.wikipedia.org/wiki/Superposition_principle under CC BY-SA license.

Reference: https://en.wikipedia.org/wiki/Superposition_principle under CC BY-SA license.

- Physics
- Systems Theory
- [1]
- Linear Systems
- Physics
- Engineering
- Beam
- Load
- Frequency Domain
- Linear Transform
- Fourier
- Laplace Transforms
- Linear Operator
- Algebraic Equations
- Linear Differential Equations
- Systems Of Equations
- Vector Fields
- Certain Axioms
- Vector Sum
- Fourier Analysis
- Sinusoids
- Amplitude
- Phase
- Green's Function Analysis
- Impulse Functions
- Impulse Responses
- Waves
- Light
- Plane Waves
- Frequency
- Polarization
- Nonlinear Optics
- Plane Waves

- Superposition Principle
- John Freeman (Georgian Poet)
- Oxford United
- Am%C3%A1lia Rodrigues
- List Of World Heritage Sites In Portugal
- Castles In Portugal
- 2015 United Nations Climate Change Conference
- Schouten Island
- Laxfield
- Oakwell
- Tiverton Preedy
- Prescrotal
- History Of Portugal (1139%E2%80%931279)
- Soviet Figure Skating Championships
- Central Powers
- List Of Museums In Portugal
- Grande Porto
- Osmar Schindler
- Audrey Hall
- 1912-13 In English Football
- Golcar
- Aerospace
- Helsinki Convention On The Protection Of The Marine Environment Of The Baltic Sea Area
- Hydrocarbon
- Buri (Germanic Tribe)
- North Atlantic Hurricane
- Roman Glass
- Milnsbridge
- Internment Of Japanese Americans
- BBC Four