Hooke's law theory question

1. Jun 14, 2010

FedEx

I am working on a theory and this thing is bothering since the past few hours...

When we write down hooke's law that is

d{2}x/dt{2} = -kx

We write down as x as the displacement from the mean position given that the mean position coincides with zero...

Now lets suppose that i have a 3D system.. And a sphere attached with various spheres... Lets say that the sphere we are interested in is (i,j). And out of the several spheres attached to ij lets say we take (i,j-1).

The question is what is my hookes law equation.. Is it

1) d{2}r{ij}/dt{2} = -[some constant][r{i,j} - r{i,j-1}]

or

2) d{2}r{ij}/dt{2} = -[some constant][r{i,j-1} - r{i,j}]

Now it is not that easy.. Cause i need to generalize this.. I have several other spheres attached with (i,j).. And if i use 1 it causes problem with some of the spheres and is okay for the rest... And if i use 2 it causes the same problem...

I cant use 1 for some spheres and 2 for others... Cause then in my 3D infinite space the equations will depend on the position of the spheres...And the eqautions would be a mess to solve and the most important it loses its beauty...

2. Jun 15, 2010