Register to reply

Superposition principle and linearity

by tardon007
Tags: linearity, principle, superposition
Share this thread:
Aug23-04, 02:57 AM
P: 4
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....
Phys.Org News Partner Science news on
Physical constant is constant even in strong gravitational fields
Montreal VR headset team turns to crowdfunding for Totem
Researchers study vital 'on/off switches' that control when bacteria turn deadly
Tom Mattson
Aug23-04, 03:30 AM
Sci Advisor
PF Gold
Tom Mattson's Avatar
P: 5,532
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:


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


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


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


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.
Aug23-04, 09:22 AM
Sci Advisor
PF Gold
Clausius2's Avatar
P: 1,479
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 priciple 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.

Register to reply

Related Discussions
Using the superposition principle Introductory Physics Homework 3
Principle of superposition Introductory Physics Homework 0
Proving the superposition principle Calculus & Beyond Homework 5
Principle of superposition Introductory Physics Homework 1
Proof of Superposition Principle Quantum Physics 13