4 ms·
It is interesting, but it's a standard way of demonstrating normal modes, or the applications of eigenvectors. I would think most physics and engineering underg
by Jabbles 13y ago
It is interesting, but it's a standard way of demonstrating normal modes, or the applications of eigenvectors. I would think most physics and engineering undergraduates have studied this.
That's not to say you shouldn't watch it, but just to put it in perspective - this is a topic studied in the 1st/2nd year of university, not a poorly-understood topic for research.
https://en.wikipedia.org/wiki/Normal_mode https://en.wikipedia.org/wiki/Normal_mode
- jstanley 13y agoIs this essentially the same as a standing wave, except 2-dimensional?
- leephillips 13y agoYes, the sand settles into the nodal lines of the pattern of vibration on the plate; those are the places where the plate is not moving. The same frequencies on a circular plate will produce different patterns.
- throwaway1979 13y agoI'm a cs person and never encountered this in school. Is this taught in engineering? Typical course names?
- btilly 13y agoAs a math person, I look at this and think "Fourier series". I encountered the ideas in both Classical Mechanics 1 (third year physics course where I took it) and Differential Equations (third year math course where I took it). It is still a nice visualization.
- diydsp 13y agoIt's very close to Fourier series, but since the "solutions" (the equilibria) are not integer multiples of a fundamental, but solutions to a 3-dimensional wave equation, it's more like "wave equation."
- btilly 13y agoFrom a mathematician's point of view it is a Fourier series. You have the property that any starting state can be divided into the sum of orthogonal components. No matter how complex the components are, that's still a Fourier series. A physicist would disagree, I am sure. But to a mathematician, an orthonormal wavelet basis is also a Fourier series.
- leephillips 13y ago"Physics".
- ndr 13y agoSystem Analysis and/or Control System.
- mcphage 13y agoForgive my ignorance, but I don't have a physics or engineering background. Given it's a well understood phenomenon, is there some way of generating mathematically what the patterns will be for a given plate shape and frequency?
- leephillips 13y agoYou solve the wave equation, a differential equation for the small-amplitude motion of the surface. The solutions depend strongly on the shape of the boundary, as is usually the case. For some shapes the patterns can be found analytically. For more complicated boundaries it's not too hard to solve this equation numerically - it's linear. Orders of magnitude easier than, say, calculating the flow of water down a pipe.
- stephencanon 13y agoYes, the shapes can be predicted by numerical solution of the governing PDE. I don't think that's what you had in mind, however. For an arbitrary plate shape, the solutions do not generally have what you might think of as a nice closed-form expression. For certain specific cases (like a square plate), these modes do have reasonably tidy descriptions.