A What Makes Vibrations So Common in Nature?

[larsa]

Vibrations are everywhere and the question is if there is some fundamental reason for this. Per example, symmetries and the least action principle are behind the conservation laws. What is the reason that vibrations are so common?

 

[ZapperZ]

Vibrations are everywhere and the question is if there is some fundamental reason for this. Per example, symmetries and the least action principle are behind the conservation laws. What is the reason that vibrations are so common?

Because the temperature around you are not at absolute zero.

Zz.

 

[larsa]

Because the temperature around you are not at absolute zero.

Zz.

I don"t mean vibrations of atoms. I mean sound propagation, water waves etc

 

[ZapperZ]

I don"t mean vibrations of atoms. I mean sound propagation, water waves etc

Then you should have been more explicit in the very beginning.

These "sound propagation, water waves, etc..." are not THAT common. These are just "physical waves". How many ARE there? They are certainly not "everywhere" in terms of different sources that generate these things.

Intrinsic vibrations, on the other hand, ARE almost everywhere.

Zz.

 

[larsa]

Then you should have been more explicit in the very beginning.

These "sound propagation, water waves, etc..." are not THAT common. These are just "physical waves". How many ARE there? They are certainly not "everywhere" in terms of different sources that generate these things.

Intrinsic vibrations, on the other hand, ARE almost everywhere.

Zz.

I admit my question is badly written . I wanted to say that harmonic oscillators can describe nature. I have read that this is because strength of fields weaken with inverse square. Is this intuition correct? ( english is not my mother tongue, i apologize )

 

[jbriggs444]

At the risk of being stupid...

If you have particles and approximate conservation of kinetic energy then there are two general possibilities. Either you have particles scattering to the winds or you have particles staying in clumps. If you have particles staying in clumps then the kinetic energy will manifest as "vibrations". No need for an inverse square principle.

Edit: Rigid rotational motion or linear motion would also be possible, I suppose.

 

[larsa]

At the risk of being stupid...

If you have particles and approximate conservation of kinetic energy then there are two general possibilities. Either you have particles scattering to the winds or you have particles staying in clumps. If you have particles staying in clumps then the kinetic energy will manifest as "vibrations". No need for an inverse square principle.

Edit: Rigid rotational motion or linear motion would also be possible, I suppose.

So you say that conservation of energy dictates that potential and kinetic energy must be interchanged?

 

[jbriggs444]

I think that I posted at cross-purposes. You are contemplating patterned vibrations and my response was not.

 

[larsa]

I think that I posted at cross-purposes. You are contemplating patterned vibrations and my response was not.

All vibrations are patterned, please explain more your insight about kinetic energy

 

[Alpharup]

There is a branch in math where we can decompose any function(either periodic or non-periodic) into sine and cosine functions called Fourier analysis. The intuition which I understood was that any vibration can be modeled as superposition of sine and cosine componenets. Each sine and cosine component has an amplitude and frequency.
let f(x) be a function
then f(x)= summation of(sine terms)+summation of(cosine terms).
In physics, any natural phenomena can be modeled( if not, we should solve differential equation for the system) as a function and this function can be decomposed into vibration(sine and cosine) components.
So, thus we can definitely say that any phenomenon in nature can be modeled as vibrations.

 

[greypilgrim]

Harmonic oscillations occur if the potential energy increases quadratically with distance from an equilibrium position. If you expand any analytical potential as a taylor series to second order, you can do away with the constant and linear (by redefining the coordinate origin) terms, ending up with only the quadratic term which leads to harmonic oscillations. Often (e.g. in solid state physics) it seems to be easier to start from here and introduce higher order terms as perturbations.

I have read that this is because strength of fields weaken with inverse square. Is this intuition correct?

Not really. Above doesn't work for 1/r-potentials because of the pole at 0, i.e. because they are not analytic at r=0.

 

[tech99]

Vibrations are everywhere and the question is if there is some fundamental reason for this. Per example, symmetries and the least action principle are behind the conservation laws. What is the reason that vibrations are so common?

It is because mechanical systems tend to have a resonance when energy can be stored either in their inertia, or mass, and their springiness. Energy can transfer between these two properties by changing between PE and KE. In many cases, objects have distributed mass and springiness, and then they behave like a transmission line. This also promotes vibrations, and can have numerous modes and frequencies of vibration. In the electrical world, conductors have inductance (involving magnetic fields) and capacitance (involving electric fields). Each of these can store energy, and vibrations occur as an exact parallel with the mechanical world. When a light switch is operated, vibrations occur in the wiring until things settle down.

 

[rootone]

... is some fundamental reason for this.

I guess that periodic oscillation between known states is the most primitive kind of ongoing change or process that can occur in any system.

 

[mfig]

Vibrations are so common because restoring forces which accompany equilibrium positions are so common.