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22 views

Does object traversing in linear motion have a constant bearing rate?

If an observer is moving at a constant rate and constant direction and another object traverses in front of the observer and is also moving in a fixed direction at a constant rate, will the bearing ...
29 views

Is it possible to have two waves of different frequency on one string?

Would this change for different Hz, Wavelengths, Speeds, or amplitudes?
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Generalized Eigenvalue Problem from linear stability analysis

I am trying to solve a generalized eigenvalue problem raised by linear stability analysis $$AV=\lambda BV.$$ $A$ and $B$ are non-symmetric complex valued matrices. The set of equations I am trying to ...
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Why is a circuit of linear elements itself linear?

A resistor's voltage is proportional to it's current. V=iR. And a source maintains a constant voltage or current. So these are linear, time independent relations. If I put combinations of them in a ...
88 views

Is there a classification scheme for linear classical field theories?

Central to a mathematical understanding of the Bogolyubov transformation is the study and classification of linear lattice field theories. What follows might be familiar to many people, but I just ...
96 views

When does the principle of superposition apply?

I assumed from my general physics courses that the principle of superposition was just an empirical fact about forces. Then I could understand that derived quantities like the $E$ and $B$ fields ...
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Why is response of system same frequency as driving force frequency

Super basic question: why does a system (to be definite, perhaps assume a collection of coupled harmonic oscillators) respond (in the steady-state, after transient effects have dissipated) with all ...
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Why superposition is useful just for linear functions?

I saw a problem which said that we have a bar between two walls and we increase the temperature. and as you know walls push a force to the bar so the length of it does not change. in the solution I ...
104 views

Physical interpretation of the canonical scalar product in linear dynamics

Consider a unforced, undamped, linear mechanical system with a finite number of degrees of freedom. Its (second order) dynamical equations can be gathered in a matrix equation $$M\ddot X + K X=0$$ ...
335 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 ...
153 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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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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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 ...
96 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 ...
107 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 ...
4k 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: ...
367 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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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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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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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 ...
13k views

How to get “complex exponential” form of wave equation out of “sinusoidal form”?

I am a novice on QM and until now i have allways been using sinusoidal form of wave equation: $$A = A_0 \sin(kx - \omega t)$$ Well in QM everyone uses complex exponential form of wave equation: A =...
2k 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 x-...
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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 ...
3k 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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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.
2k 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 ...
3k 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 ...
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 \$\...
666 views

Can the Kramersâ€“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 ...