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Superposition | MIT Physics | Quantum Physics | Adam Adams | Lecture One
MIT Physics Lecture One | Quantum Physics | Adam Adams | SuperPosition
Superposition - The net response induced by two or more stimuli for any linear system is equal to the total of the responses induced by each stimulus separately. This is known as the superposition principle, or superposition property. in order for input (A + B) to produce response (X + Y) if input A produces response X and input B produces response Y.
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Physics | Superposition
Any linear system, including algebraic equations, linear differential equations, and systems of equations of those types, is subject to the superposition principle. Numbers, functions, vectors, vector fields, time-varying signals, or any other object that complies with a set of axioms can all be used as stimuli and reactions. Note that a superposition is understood as a vector sum when vectors or vector fields are involved. Because of their definition, all linear operations done to these functions, including gradients, differentials, and integrals (if any), automatically hold if the superposition holds.
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Relation to Fourier analysis and a like methods
It is frequently easier to compute the reaction when a highly general stimulus (in a linear system) is written as the superposition of stimuli with a specific and basic shape. For instance, the stimulus in Fourier analysis is expressed as the superposition of an infinite number of sinusoids. The superposition principle allows for the independent analysis and computation of each of these sinusoids' responses. (In general, the response's amplitude and phase diverge from the stimulus's, but it still has the same frequency as the stimulus.) The response to the initial stimulus is the total (or integral) of each individual sinusoidal response, according to the superposition principle. Another typical example is when the stimulus is expressed as the superposition of an unlimited number of impulses in Green's function analysis. Superposition of Waves
Waves are typically defined as changes in certain characteristics across time and place, such as pressure in sound waves, height in water waves, or electromagnetic field in
light waves. The wave itself is a function that indicates the amplitude at each point, and the value of this parameter is referred to as the wave's amplitude.
Any system containing waves has a waveform at any given time that depends on the system's initial circumstances and sources, or any external influences that may be causing or affecting
the wave. The equation describing the wave is linear in many circumstances (the classic wave equation being one such example). The superposition principle can be
used when this is the case. In other words, the net amplitude was the cause.
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