Superposition Principle

In physics and systems theory, the superposition principle, also known as superposition property, states that, for all linear systems, the net response at a given place and time caused by two or more stimuli is the sum of the responses which would have been caused by each stimulus individually. So that if input A produces response X and input B produces response Y then input (A + B) produces response (X + Y).

Superposition is one of two requirements for a function to be linear. A linear function is one that satisfies the properties of superposition (additivity) and homogeneity of degree 1 (scalar multiplication) which are defined as

(superposition)

for scalar "a".

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. Because physical systems are generally only approximately linear, the superposition principle is only an approximation of the true physical behavior; it provides insight for typical operational regions for these systems.

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 which satisfies certain axioms. Note that when vectors or vector fields are involved, a superposition is interpreted as a vector sum.