# 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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### 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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### Counting number of Antinodes for Modes in 2D

In 1D cases for standing waves, if we have the 3rd harmonic on a string of length L, then there are 3 antinodes and 2 nodes in between. This means, for each wavelength, we can establish a relationship ...
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### Initial values for oscillations about a point (normal modes problem) [closed]

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 ...
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### Which Hamiltonian systems are intrisically linear?

What physical properties has a dynamical system whose equation of motion are linear? When does it exist a change of coordinates which turn the equation of motions in a linear system? My teacher says ...
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### sound waves , standing waves,wind chimes [closed]

I don't know how to approach this problem. It's been bothering me for months. The answer seems to be the rod with shortest length
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### Transverse modes in optical resonators

Im struggling with understanding transverse modes in an optical resonator or laser. Hopefully you can solve this mystery for me. Thank you very much! As far as I know, there are two types of modes: (...
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### Normal modes: how to get reduced masses from displacement vectors, atomic masses and vibrational frequencies

I'm calculating normal vibrational modes in a large molecular system. My goal is to obtain, for each normal mode, the vibrational frequency, the list of displacement vectors and the reduced mass. I'...
In a hollow rectangular waveguide, we may either propagate transverse electric modes (TE$_{mn}$) where we have electric standing waves quantified by m and n in each direction, or transverse magnetic ...