1. You can get velocity,height and mass for each particle in the simulation, so that you can calculate their kinetic energy and potential energy individually. And the sum of those will be the energy for the whole system.
2. EJS help you calculate the integration numerically. It would not obtain analytic equation for you.
3. If array were used in the evolution equation, for example  [code]d x[i]/dt =v[i][/code], then the whole array x[n] will be evaluated.
If you do not want some of the value changed, you need to set their derivate value to zero.
For example: [code]for (int i=5;i<n;i++)v[i]=0.; [/code]

Did you check out [url=http://www.phy.ntnu.edu.tw/ntnujava/index.php?topic=362.0]Circular Spring Thing[/url]?
It is almost the same as your circularspring.xml (number of springs can be changed from 3-60).