Damped Cyclic Phenomenon Model

[fancygirl2]

If you are given 4 points, say (x1,y1), (x2,y2), (x3,y3), and (x4,y4) how would you find a damped cyclic model (equation) for these data points?

 

[tkhunny]

If it were me, I think I use the methods in the book or the ones I just learned in class - had I been paying attention.

Please provide substantially more specific information and show your work.