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1answer
116 views

Principle of superposition and QED

For finding a net force on a charge when it is in influence of many charges we simply do vectorical addition of all individual interaction of that charge with others. That's what is principle of ...
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1answer
48 views

General second order system and mass spring damper in control theory

I am studying control theory and most textbooks and web resources define a general second order system in the $s$ domain as $$ G(s) = \frac{\omega_n^2}{s^2+2\,\zeta\,\omega_n\,s+\omega_n^2} \, .$$ ...
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21 views

Initial conditions for second order ODE with complex stiffness

I tried this on Math Stack Exchange. I'm trying to find initial conditions to ensure systems of the form stay bounded $$\ddot{x}_i+\sum_{j=1}^N k_{ij} x_j = 0, \quad k_{ij} \in \mathbb{C}.$$ For ...
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0answers
30 views

Kirchoff's circuit law matrix representation

A couple of recent Kirchoff's law questions with wacky geometries got me thinking. "Solving" any circuit that consists only of resistors and e.m.f. sources can be reduced to solving a linear system of ...
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2answers
121 views

Linearity in Quantum Mechanics that make superposition possible

As a beginner in QM, all the video lectures that i have seen talk about superposing wave functions in order to get $\psi$. But from what i know from linear algebra, the system must be linear in order ...
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1answer
60 views

Variable Gear System [closed]

I have a variable speed gear system with 4 primary parts. I need to find the relationship between input rotational speed (wi) to output rotational speed (wo). Fig. 1 shows three of the primary ...
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1answer
100 views

Can I state that $\Psi (x_1, \dots , x_n,t)= \sum_{i=1}^n a_i \psi (x_i,t) $ via superposition?

Given that the hamiltonian $\hat H$ of a system is a linear operator and $\dot \psi (x_i,t)$ does not depend on spatial coordinates $x_1, ..., x_n$ with bases $\hat e_1, ... , \hat e_n$ can I state ...
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2answers
227 views

Why do wave functions need to be normalized? Why aren't the normalized to begin with? [duplicate]

Before I started studying quantum mechanics, I thought I knew what normalization was. Just pulling off Google, here's a definition that matches what I've understood normalization to mean: ...
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1answer
141 views

Superposition in classical Mechanics

I watched a video in YouTube solved these problem using superposition First he fixed the bottom rope and found the accelearations Second he fixed the upper pulley and found the accelerations Third ...
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0answers
32 views

Non-linearity of energy conversion efficiency

I have a very general question to all of you. I am wondering if there is any basic physics principle that would state that energy conversion efficiency will be always non-linear (for the practical ...
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2answers
46 views

What dynamical system could this $\dot y = \alpha(y-\lambda), y\geq \lambda$ equation describe?

Just out of curiosity, can anyone identify electrical, mechanical, chemical, etc process that is governed by a differential equation of the form $$\dot y = \alpha(y-\lambda), y\geq \lambda$$ where ...
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0answers
56 views

Berry curvature and linear response functions

Let $\hat{A}^i (i = 1, . . . , n)$ be a set of hermitian observables and $F_i$ a corresponding set of external fields that are linearly coupled to $\hat{A}^i$. Starting from the ground-state at $F_i = ...
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3answers
292 views

The ubiquitous Planewave Ansatz

In physics, the planewave ansatz (meaning: an educated solution guess) is very ubiquitously used, when solving differential equations, in different domains of physics. E.g. to solve the dispersion ...
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1answer
43 views

What makes a system linear?

Lately I have been interested in Image Processing, and I started by following this course: https://class.coursera.org/digital-001, which is quite awesome in my opinion. But in weeks 2, Linear ...
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2answers
164 views

Would magnetic flux be necessary for analogous systems?

I learned about the analogousness between mechanical and electrical systems a few months back (with the help of Feynman). Yesterday, my professor was lecturing about this topic, when she told that ...
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1answer
424 views

Why doesn't amplitude affect the speed of sound?

I understand why amplitude doesn't affect the speed of the sound AFTER the 'leading compression'. The extra force provided on one stage of the cycle is countered on the other stage. But shouldn't the ...
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0answers
117 views

Is strictly harmonic 2D lattice made of Hooke springs possible?

If we connect a set of point masses in a 1D lattice with Hooke springs and consider longitudinal oscillations, we'll have a strictly harmonic system, for which there exist eigenmodes and the frequency ...
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0answers
113 views

Meaning of Eigenvalues/Eigenvectors of a linear system of equations

I have a 41x41 system of linear equations (inhomogen) which I derived with Eureqa by describing the timecourse of fMRI haemodynamic data from a brain area as a function of the timecourses of 40 other ...
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1answer
228 views

Principle of Superposition for driven oscillator

So I understand the the Superposition Principle states that all the forced oscillations, as determined by multiple external forces, are to be added up in order to get the entire solution. However, ...
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1answer
204 views

Superposition theorem

Is superposition theorem applicable for circuits having semiconductor components like diodes, transistors, etc.?
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136 views

Physics and Linear Differential Equations

Why in physics, most of the physical systems are modelled by linear differential equations?
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0answers
75 views

Multiple meanings of polarizability?

There's a concept in linear response theory called the polarizability $\chi$ $$\tag{1} \rho_{ind}=\int \chi(\vec{r},\vec{r}',t-t') V_{ext} \: d\vec{r}' dt' $$ where $\rho_{ind}$ is the induced charge ...
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2answers
209 views

Linearized equations

What is $V_{\alpha\beta}$? And what is a symmetric, positive definite potential energy matrix? And why is there a linearized equation like this?
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4answers
17k views

Transverse Magnetic (TM) and Transverse Electric (TE) modes

I'm reading and working my way through "Plasmonics Fundamentals" by Stefan Maier and I've come across a step in the workings that I'm struggling to understand when working out the electromagnetic ...
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1answer
148 views

Why linear wave equation does not have solitonic solutions?

As many people define solitary waves they are localized pulses that propagate without changing the shape. As far as I know the same pulses exist in ordinary wave equation ! why should we look for ...
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2answers
230 views

“Complex Variables Method” in Diff. Eq. - Justification and physical meaning?

A common method of simplifying calculations that involve differential equations - particularly involving oscillation - is to replace $\cos(\theta)$ with $e^{i \omega t}$, evaluate, and then take the ...
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1answer
2k views

Is squared motor gearbox ratio proportional to inertia ratio?

I read an interesting article http://m.machinedesign.com/news/motor-sizing-made-easy It is very interesting, but I can not follow the 2nd last paragraph. I don't understand why it is true. ...
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2answers
483 views

Linearity of Quantum Mechanics?

The proof of the No-Cloning Theorem states "By the linearity of quantum mechanics, ..." -- Could someone please give me a rough sketch/outline of what this means? Does it have to do with the Hilbert ...
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0answers
90 views

How to get general relativity from linear gravity theory?

I know someone had done this study. Namely the field approach to general relativity. We can easily get an linear gravity theory. But it will be very complicated when we consider the ...
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2answers
144 views

Linear quantization in quantum electrodynamics?

This is a continuation of this question. What would be an example of linear quantization used on quantum electrodynamics? I ask this because QED is a nonlinear theory.
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2answers
160 views

Undamped oscillations. Why is the solution a linear combination of $\sin()$ and $\cos()$?

$ma = mg - cx$, where $x(0) = x_0 = 0$ is the position in which there is no tension in the rope. $dx/dt = v_0$ for $t = 0$; $v_0$ is a known constant. The discriminant of the characteristic ...
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0answers
285 views

linear response for a simple harmonic oscillator

Really sorry for this simple question, but I think it will be useful/interesting in general. Consider a quantum simple harmonic oscillator. Add a perturbation $H_I = -\lambda \hat{x}$ Calculate ...
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3answers
347 views

Is normalization consistent with Schrodinger's Equation?

Schrodinger's Equation does not set a limit on the size of wave functions but to normalize a wave function a limit must be set. How is this consistent physically and mathematically with Schrodinger's ...
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3answers
81 views

Solving systems of equations in dynamics

I have an exam in two days for first year university physics. Often for dynamics problems, I am required to solve algebraic systems of equations by hand, and this can be very daunting. When I see ...
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1answer
1k views

What is the Laughlin argument?

The fundamental question is Why is Hall conductance quantized? Let's start with the Hall bar, a 2D metal bar subject to a strong perpendicular magnetic field $B_0$. Let current $I$ flow in the ...
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2answers
219 views

Many faces of linear response theory

I have seen two forms of linear response: One is in the calculation of susceptibilities using Green functions. The other is in the evaluation of response currents, say, London current of a ...
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4answers
2k views

What does superposition mean in quantum mechanics?

What does superposition mean in quantum mechanics? When I say $A+B=C$ (forces). I can mean push something with force $A$ + force $B$ together, and that is same as I push it with force $C$. But when ...
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1answer
154 views

Microphones, Loudspeaker and their analogies to spring mass system

I have just started studying Microphones and Loudspeakers. I need a good text to refer which can explain their mechanical analogies with simplicity and basics too.
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1answer
1k views

Is the universe linear? If so, why?

Simple question, I'm trying to build a quantum memory system that utilizes the superposition principle to model specific phenomenon I am trying to predict, anyways, my question is this. Is the ...
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4answers
2k views

Why is the Principle of Superposition true in EM? Does it hold more generally?

In the theory of electromagnetism (EM), why is the principle of superposition true? Can we read it off from Maxwell's equations directly? Does it have any limit of applicability or is it a ...
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1answer
1k views

Matrix solution of an equivalent resistance circuit problem

Start with a set of points $x_1, x_2, \ldots$ that are connected by wires with some resistance. Represent the resistance by a conductance matrix (conductance being one over the resistance), where ...
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3answers
495 views

Can the Kramers–Kronig relation be used to correct transfer function measurements?

In experimental physics, we often make measurements of linear transfer functions; these are complex-valued functions of frequency. If the underlying system is causal, then the transfer function must ...
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5answers
1k views

Linearity of quantum mechanics and nonlinearity of macroscopic physics

We live in a world where almost all macroscopic physical phenomena are non-linear, while the description of microscopic phenomena is based on quantum mechanics which is linear by definition. What are ...