# Questions tagged [linear-systems]

A linear system is a mathematical model of a system based on the use of a linear operator. A system is linear if and only if it satisfies the superposition principle, or equivalently both the additivity and homogeneity properties, without restrictions.

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### Applications of Signal and System theory

I recently heard a lecture about Signals and Systems and find the subject extremely exciting. I would like to do more in this direction, so I would be interested to know in which modern research area ...
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### Is there any fundamental reason why acceleration is a linear function of external forces?

Perhaps a trivial question, but it is something which I couldn't ever grasp ever since beginning physics. Why exactly should Newton's second law be linear in application of all the external forces? ...
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### Complex physical quantities

I have a question regarding complex physical quantities. Why do we consider only the real part of a complex physical quantity? Why not the modulus? Since, for $z=a+bi$, we have $|z| = \sqrt{a^2+b^2}$, ...
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### Why potential due to system of charges is scalar sum?

Suppose there are three point charges $q_1,q_2,q_3$. We have to find potential at point $P$. So we do scalar sum of all potentials at that point taking one charge at a time. But I am saying that, when ...
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### What is a linear system?

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Say we have a charged shell A (radius $R$) that is present within another charged shell B (radius $2R$). The charged shell A has a net charge $Q$ and the shell B has a net charge $3Q$. Taking shell A ...
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### What is proof of principle of superposition of waves on a string?

I was studying waves on a string and there was this 'Principle of Superposition of Waves' which states that the net displacement of a point is equal to the vector sum of displacements caused to the ...
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### In classical physics (classical electrodynamics), why linearity of Maxwell's equations prevent interaction of electromagnetic waves?

In classical physics (classical electrodynamics), electromagnetic waves don't interact. In quantum mechanics, they could. In this article on light-by-light scattering: https://arxiv.org/abs/1702.01625 ...
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### Why does the dependence of Coulomb force on the medium not conflict with the superposition principle?

Why does the dependence of Coulomb force on the medium not conflict with the superposition principle? As I have been told (and checked myself on the web including this website), the Coulomb force ...
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### RL circuit with AC source transient

I have a simulation of RL circuit connected with an ac source. Any one can tell me please that why the peak of the current during the first positive half cycle is higher than the peak of current ...
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### Transient in RL circuit

Why the transient current will die off in series RL circuit with AC source? Every time the ac voltage source reverses direction so does the current and the current has to pass through the same ...
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### Do linear theories have infinitely many solutions?

It is said that, in a linear theory, you can add any number of solutions to still find a solution. So, say I initially found three solutions to a linear theory, and I call them a1, a2, and a3. Now I ...
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### How does the linearity of the Schroedinger equation reflect the interactions?

There is a common lore that linear equations describe non-interacting systems, why non-linearities correspond to non-trivial interactions. My (loose) question is how is that compatible with the ...
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### Throwing a baseball at a car and it staying there [closed]

I was recently asked the following question in a physics contest: For some odd reason, you decide to throw baseballs at a car of mass $M_i$, which is free to move frictionlessly on the ground. You ...
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### Direction of current using superposition method

I have to calculate the current I and the voltage between a and b using the superposition theorem. I can solve this directly by calculating the voltage between points, but I have to do it with that ...
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### Three masses with 2 springs in 1D

Consider three arbitrary masses attached by two different springs in vacuum, starting at arbitrary initial positions with no initial velocities. Is this system chaotic? Is this system analytically ...
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### Can concepts like "critical damping" or "resonant frequency" be applied to more complex systems than just a spring and damper in parallel?

I am trying to do some modeling analysis by representing materials with parallel systems of springs and dampers. In the simplest case with just one spring parallel to a damper, we have the traditional ...
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### Does Lagrangian follow superposition principle?

In other words: is the Lagrangian of a composite system the sum of the Lagrangians of its components? It shouldn't be, since it's energy. But then we lost one of the most important principles in ...
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