# Questions tagged [normal-modes]

Normal modes refer to fundamental patterns of motion of a system which oscillate at fixed, well defined frequencies. They may be used as building blocks for more complicated motions.

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### Terminology question: in-phase or out-of-phase?

Suppose that in a chain of many coupled oscillators, the displacements of two consecutive particles, in a normal mode of oscillation with frequency $\omega$, are given by $$x_p(t)=A_pe^{i\omega t}$$ ...
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### Why is any arbitrary motion of a coupled oscillator writable as a linear combination of its normal modes? [duplicate]

Consider the following example of a coupled oscillator. Let two identical pendulums, each of length $\ell$ and mass $m$ be connected by a spring of force constant $k$. The system has two normal modes ...
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### Coupled Oscillator Period [closed]

I was studying an example of a coupled oscillator the other day, namely two identical masses attached to three springs, the lateral ones of which with the same elastic constant, when I came across the ...
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### Why do guitar strings behave so nicely?

To explain the harmonics on a guitar string, we use 2D models of the string. For example we assume that the string can only go up and down. But the string is inherently a 3D object and it could ...
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### Do normal modes need same amplitude?

Suppose we have a coupled pendulum of 2 masses. I understand that the first normal mode they oscillate together, in phase, with the same frequency. However, do they need to have the same amplitudes? ...
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### Deriving the parameter $\exp(\eta)$ in eq. (2.9) from "Illustrative example of Feynman’s rest of the universe"

I'm working on research on the Entanglement in Coupled Harmonic Oscillators when I stumble upon the research paper "Illustrative example of Feynman’s rest of the universe" https://doi.org/10....
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### The notion of TEM, TE and TM modes in an arbitrarily shaped cavity

In order to define the usual modes of EM waves in a confined space, TEM, TE and TM, one must have a well defined notion of "transverse" and "longitudinal" in the system. In the ...
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### What are the normal modes of a velocity-dependent equation of motion?

I'm trying to find the normal models of a particle with charge $q$ and mass $m$ in a $3$-dimensional harmonic oscillator potential with an applied uniform magnetic field $B=B_0 \hat{z}$. The potential ...
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### Generalised coordinates

I am working on a scientific project for my university and I am reading a german paper (Karas: "Platten unter seitlichem Stoß") which makes use of generalised coordinates. It's about an analytical ...
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I have the Lagrangian $L=\frac{1}{2}(\dot{x}^2+\dot{y}^2) -7x^2+2xy-\frac{11}{2}y^2$. So the two equations of motion are $\ddot{x}+14x-2y=0$ and $\ddot{y}-2x+11y=0$. Hence the general solution (by ...