Talk:Normal mode

A Quite Biased Definition
Several comments:
 * 1) I wonder, how the definition can be less biased to mechanical systems. The definition is both applicable to electromagnetic fields and structural building analysis. Also, several part of the article define this as 'displacements' which only holds true for the mechanical case.
 * 2) A mathematical definition would also be good. Which is given, but only for the quantum solution. A sinusoidal decomposition from a dynamical system should be proper here as startup.
 * 3) A Mode has NO relation nor requires to have an oscillating system!. The system don need to 'oscillate' -such as the music case-. Instead, a mode IS an oscillatory term itself. IF can or cannot be dominant is another history...
 * 4) The Mode is indeed applicable to dynamical systems belonging almost every field of physics and engineering, mainly:
 * 5) * Electromagnetic systems
 * 6) * Mechanical/Vibration Systems
 * 7) * Structural Systems
 * 8) * Wave Theory
 * 9) * Optics Systems
 * 10) * Quantum Mechanics Systems
 * 11) * Molecular Systems
 * 12) A mode is a linear representation. Please note, thus, that Nonlinear Modal decomposition exists, linearizing when the decomposition is more appropriate. An example are nonlinear damping systems. Under this case, of course, the decomposition is not discrete, but continuous on the coordinate space.
 * 13) The article does not distinguish between the 'Mode' and its 'Excitation'. A mode is always a decomposition, which by definition has its own frequency fn, and which can or cannot be dominant -i.e. seen at direct sight on the 'water'-.
 * 14) The article does not talk about the 'stability' of a mode, on the dynamical sense. IF I excitate the water at fn, the n mode will 'dominate' and will be 'seen'. If i excitate the water at fn+df, under a certain df, the n mode will still -if the mode is stable- dominate, it will 'resonate', and behave like a 'pole'. IF the mode is 'unstable',the mode never will be dominant, it will not 'resonate', will behave as a 'zero'.
 * 15) Normal and Superposition requires -at least slightly- to be defined under this context. The modes on this context is simply a decomposition of a Dynamical Model, and it is normal in the metric of the representation -its Hilbert space, etc.- Hence, the mathematical and physical link for the definition will be straightforward...
 * 16) Resonance is the phenomenon under which a system oscillates with amplified amplitudes. Resonance, thus, ocurrs for modal frequencies. This is just tacked on the definition, but should be clarified.
 * 17) The coupled oscillator shall be presented as example, not as a section.
 * 18) Standing Waves ARE modes!. Under systems with 'compact' boundaries -such as an interval, a closed 2D circle membrane/square/etc., etc.- a mode is indeed represented as an standing wave. Which i would like to have here is a TRAVELLING WAVE, which are special types of modes, on which the time is another variable taking part. Because here we don't have 'amplitudes' for 'points', we cant call it a mode....
 * 19) An electromagnetic section, with their classical TE1, TM1, nomenclature etc. and some links about this topic, would be REALLY ubiquitous here. Also, some examples for field cavities would be appreciated.

If accepted, I could add most of these addendums. Hyprwfrcp (talk 04:48, 21 May 2015 (UTC)

Description of motion relative to diagram please
Someone please add which motions of the system above the two normal modes represent! --128.252.125.40 19:41, 27 September 2007 (UTC)

pick your favorite:



(never made a mechanical diagram before.) - Omegatron 14:17, Jul 21, 2004 (UTC)

All are nicely down. I vote for the third. MathKnight 16:25, 21 Jul 2004 (UTC)

Isn't it a way you can crop the 3rd one? MathKnight 18:07, 21 Jul 2004 (UTC)

I consider myself reasonably informed, but I'm completely daunted by the maths on this page. Isn't there another way to explain what this means? Electricdruid 00:36, 29 January 2006 (UTC)


 * I improved it a bit, I hope. Pfalstad 05:02, 29 January 2006 (UTC)


 * If "reasonably informed" includes a solid understanding of ordinary differential equations and just a little bit of linear algebra, you should be able to get though this. But if you took your math classes and forgot it all, you are no longer reasonable informed. --neffk 19:39, 21 July 2006 (UTC)


 * Neffk: Electricdruid is probably representative of the typical visitor to Wikipedia; a middle-of-the-bell-curve sort of guy. Someone can easily have an I.Q. of 100+ and be “reasonably informed” and not be mathematically inclined. Your dismissive response was the sort of terse cheap shot that people with a sense of anonymity occasionally resort to.  I suspect your comment momentarily made you feel elite and special. However, if a Wikipedia article—or any article in any encyclopedia—is talking over the heads of the audience, it can probably benefit from the addition of some explanatory text in the math section.  The whole point of technical writing is to convey complex issues in clear, concise terms.  It's only too easy to simply regurgitate formulas out of text books. One can often tell whether a contributor to a math-related section in a Wikipedia article was trying to effectively convey the formula by whether or not they bothered to list what each of the formula's terms means (as well as the required units of measure to make the formula work). When authors omit these (which unfortunately occurs way too often in Wikipedia), they either don't understand the formula well enough themselves to do so, or they are lazy, or they are using Wikipedia as a vehicle to inflate their egos because they feel they are part of an elite club that understands what each of the *secret* terms in the formula means. Upon seeing the comment from Neffk, Pfalstad waded in and made some improvements.  What was your contribution? A cheap shot. Nice going.   Greg L 15:02, 4 October 2006 (UTC)

coupled systems
The article is nice but it seems to imply a lots of things and not really state much... On a slightly different note, perhaps it should be mentioned at the very beginning that normal modes generally refer to systems of coupled oscillators? And that its not simply a matter of frequency but also the relative phase differences?

For example three springs connected in such a way that masses are on the points of a triangle. One possible mode would be the 'breather mode' where all the springs compress and extend in phase. Another would that one spring contracts while the other two extends. Or maybe the coupled pendulum case may be more easily related as swings (but personally I find it less intuitive in terms of eigenvectors - its so easy to choose another basis set, I'm more aware of the eigenvectors more oscillators are involved! ) And that these modes form a complete set of `different types of oscillations' - the eigenvectors, from which all possible forms of oscillations may be constructed.141.2.215.190 19:12, 4 January 2007 (UTC)

wider context
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)

Merged
Well I merged it.

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

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)