What defines a mode of vibration and distinguishes one from another?

[Zacarias Nason]

This is a really silly/very basic question but I'm having trouble finding a clear, concise definition of a "mode of vibration"; assuming the same object that is vibrating is being discussed each time, are the only things characterizing a mode of vibration the waveform, the frequency of the mode, and the energy?

What is a good definition of what a mode of vibration is that gives enough information to distinguish one mode from another?

 

[andrewkirk]

It depends on the context. But usually, when modes of vibration are discussed, it means 'normal modes', which are eigenvectors of the relevant linear operators.
For multi-dimensional surfaces like drums, that can get complicated.
But for a one-dimensional item like a string secured at both ends, the frequency is all that is required to characterise a normal mode of vibration. The waveform will always be a sine curve, and the amplitude and energy don't matter - all sine waves with the same frequency are regarded as being the same mode, regardless of amplitude or energy.
The frequencies of the different normal modes will all be positive integer multiples of the lowest frequency at which the string can vibrate with a standing wave.

 

[Zacarias Nason]

Thank you! And one last question; modes 1-3 here are apparently normal modes, just, as you said-sinusoidal standing waves, just of different frequencies. Is there a general name for the other modes? What do you call the modes of vibration that *aren't* normal modes, and from a glance, are the other modes not normal modes?

 

[M Quack]

Other modes would be superpositions of normal modes.

If you search for videos of Chladni plates you will see some nice demonstrations of standing waves and vibrational modes.

 

[Zacarias Nason]

So, essentially all modes are either normal modes themselves or a combination of normal modes, then?

 

[andrewkirk]

That's correct Zacarias.