Mechanical system with simlar phyysics of neutrion flavor mixing.

[Spinnor]

Mechanical system with similar physics of neutrino flavor mixing. Pull one mass down while holding the others at their rest positions. Now let them all go.

See system here (don't know how to add images):

https://picasaweb.google.com/andyeverett57/August282011

Sorry for the spelling in the title, could not edit or cancel, the title should read:

Mechanical system with similar physics of neutrino flavor mixing.

 

[Spinnor]

I think k_12, k_23, and k_31 can be the same and we have physics more similar to flavor mixing physics?

Thanks for any help!

I think the system in my drawing need to be tweaked? Maybe the masses are the same but the springs k need to change?

 

[Spinnor]

So let's make the system of three coupled harmonic oscillators as general as possible, its Lagrangian should be:

L = {[m_i*v_i^2/2 - k_i*x_i^2/2]i=1,2,3} -{[k_ij*(x_i-x_j)^2/2]i,j=12,23,31}

the kinetic energy of the masses minus the energy in the springs.

This Lagrangian has too much freedom, the masses and 6 spring constants can be different. We need to reduce this freedom?

Any thoughts?

 

[Spinnor]

The goal is to reproduce a graph similar to:

http://en.wikipedia.org/wiki/File:Oscillations_electron_long.svg

From:

http://en.wikipedia.org/wiki/Neutrino_oscillation

 

[Spinnor]

Looks like the drawing of my system was set not to be viewed by others, think that is fixed now, sorry.