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Results tagged with normal-modes
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user 129209
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.
5
votes
Simple coupled quantum harmonic oscillator
The Hamiltonian is a quadratic form both in the momenta and in the coordinates. You can decouple the problem by using the principal axis theorem on the coordinates to obtain generalized coordinates. F …
- 17.1k
2
votes
Accepted
What is a mode? Regarding electromagnetic waves in a closed cavity
The different modes of electromagnetic waves in a cavity correspond to different eigenfunctions of the solutions of the electromagnetic wave equation given the boundary conditions of the walls of the …
- 17.1k
1
vote
Finding the eigenfrequencies of a vibrating sphere
I did not check your algebra in detail. In essence you have the problem of small oscillations of a coupled system of mass points with linear forces between them described by a quadratic potential in t …
- 17.1k
1
vote
Energy Conservation of waves at a boundary
The frequencies are the same left and right of the boundary because you assume only sinusoid time variations $∝\exp{(i\omega t)}$ with angular frequency $\omega$.
The strings are connected at the jun …
- 17.1k