Talk:Normal mode

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Dynamic modes are important to any system governed by linear homogenous differential equations, this includes aircraft stability modes, shimmy, flutter, hunting, etc. I have used this article as a cross reference from Gyro monorail but it is not sufficiently general. The alternative reference to Eigenvalues is really too arcane, even for the above average reader who could cope with the maths in the monorail article.

May I suggest introducing the subject with reference to the classical eigenvalue problems. The first is the ancient problem of how slender a column can be made before it will buckle. This dates back to the ancient Greeks, who considered slender columns to be aesthetically more pleasing than the squat pillars characteristic of Egyptian architecture. The solution is the Euler buckling theory, which is a simple eigenvalue problem. There is an infinite number of failure loads, each corresponding to a different deformation shape. Each deformation shape is a mode. The fact that we are only usually concerned with the lowest buckling load is irrelevant - we can always imagine a situation where a large load is suddenly applied - invoking a higher order mode.

Staying with the ancient Greeks, the first recorded eigenvalue problem is the prediction of the pitch of a taut string when it is plucked. Pythagoras used the ratios of string lengths to relate number to harmony. Here again, the string has an infinite number of modes which may be excited by plucking or bowing. Both the strut and stretched string may be illustrated with diagrams of sinusoidal deformations. After all a mode is essentially a shape which characterises the displacement of the system from its undisturbed state, and a frequency of the associated motion (or, in the strut case an associated buckling load).

These descriptions could be backed up by mathematics, but this should not be necessary. After all, most school kids are aware that a six inch ruler is harder to buckle than a 12inch ruler. Most people have noticed that blowing harder into a recorder causes the pitch to suddenly double. I suggest that appeal to everday experience, rather than to apparently obscure and esoteric applications is more likely to convey the idea to a wide audience. Gordon Vigurs 11:25, 7 March 2007 (UTC)[reply]

Merged

Well I merged it.

Kallog (talk) 03:57, 20 March 2010 (UTC)[reply]

Some clarification and additional external link

hope you're all happy with my clarification on why the determinant must be zero. Reading the article, I found it was easy to mistakenly think that the matrix would have to be invertible, as the singular link in fact links to the article about non-singular matrices.--Ask a Physicist (talk) 17:01, 3 December 2011 (UTC)[reply]

Coupled oscillators

The section on coupled oscillators has no sources. Goldstein setcn 10.4 treats "Free vibrations of a linear triatomic molecule. The math is very similar, with only the addition of the center of mass motion. This example could added or it could replace the existing one. Johnjbarton (talk) 00:29, 15 September 2024 (UTC)[reply]