# Mechanical system with simlar phyysics of neutrion flavor mixing.

1. Aug 28, 2011

### 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):

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.

Last edited by a moderator: May 5, 2017
2. Aug 28, 2011

### 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?

Last edited: Aug 28, 2011
3. Aug 28, 2011

### Spinnor

So lets 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?

Last edited: Aug 28, 2011
4. Aug 28, 2011

### Spinnor

Last edited: Aug 28, 2011
5. Aug 28, 2011

### Spinnor

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