Superposition principle and linearity

In summary: Hi! The superposition principle states that if you have two or more inputs that can cause an output, you can calculate the resultant force by adding the individual forces. This principle is used in many sciences, like mechanics, electromagnetism, structural engineering, electrical engineering, and other fields that are governed by linear equations. Superposition principle is not used in nonlinear sciences, like fluid mechanics, combustion theory, and nonlinear physics.
  • #1
tardon007
4
0
hello folks!

this is my first post on the forums and I kick off with an interesting question...

I had been coming across the principle of superposition for quite some time and to admit frankly didn't ever understood it.

The most abstruse aspect is to comprehend how can to different inputs(take 'em as forces for the moment) set up out puts, totally ignorant of each others presence?

Can some one throw some light on this... Also , has the superposition principle been deduced emperically or has there been some physics behind the existence of the postulate...
 
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  • #2
Hi, and welcome to PF.

Superposition for forces is a direct consequence of the law of vector addition and of the linearity of Newton's law. That is, if you take your inputs to be forces (let's say there are 3 of them) and your outputs to be accelerations, what you have is the following:

F1=ma1
F2=ma2
F3=ma3

If you add these up to get the resultant force F, you get:

F1+F2+F3

which of course is a vector sum. Now on the other side of the equation you get:

ma1+ma2+ma3

Since Newton's second law is linear, we have:

F=ma,

where a is the resultant acceleration.

Superposition in other systems relies similarly on either scalar or vector addition, and on linearity of the system in question. If a system is nonlinear, superposition will not hold.
 
  • #3
Hi tardón!

Superposition principle is a famous topic in many science areas: mechanics, electromagnetism, structural engineering, electrical engineering, electronical engineering and other parts that are governed by linear equations.

Surely, superposition principle had a mathematic fashioned way of being discovered. Former physicians knew about the linearity of the governing equations of some phenomenas. Although it is certain too that all this equations were built up over experimental researches. So that, former physicians must have had some empirical verifying of the superposition principle.

By the way, superposition principle is not employed at all in nonlinear sciences, like fluid mechanics, combustion theory, nonlinear physics and so on.
 
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What is the superposition principle?

The superposition principle is a fundamental concept in physics and engineering that states that the total response of a linear system is the sum of the responses caused by each individual input.

What is linearity?

Linearity is the property of a system where the output is directly proportional to the input. In other words, if the input is doubled, the output is also doubled. This property is necessary for the superposition principle to hold.

How does the superposition principle apply to waves?

In the context of waves, the superposition principle states that when two or more waves overlap, the resulting wave is the sum of the individual waves.

What are some examples of systems that exhibit linearity and the superposition principle?

Some examples of linear systems that follow the superposition principle include simple circuits, ideal springs, and ideal gases. These systems have a linear relationship between the input and output, allowing for the principle to be applied.

What are the limitations of the superposition principle and linearity?

The superposition principle and linearity only hold true for linear systems. Nonlinear systems, such as chaotic systems, do not follow these principles. Additionally, the superposition principle is limited to systems with small amplitude inputs, as large inputs can cause the system to behave non-linearly.

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