How to turn a table into an equation?

[StillDumb]

Hey guys
Sorry if this is a dumb question, but how do I turn a table into an equation? I need the line or curve to fit the points. And I need the line or curve to periodically go back to zero in between each point. Below are my numbers and straight line slopes.

x y Slope
1 20
2 8 -12
3 9 1
4 19 10
5 27 8
6 9 -18
7 19 10
8 27 8
9 1 -26
10 27 26
11 20 -7
12 5 -15
13 19 14
14 20 1

Questions:
1) Since I want the equation to periodically return to zero in between each point, is there a way that I can model this as a sin or cos wave (or a combination)? That would make sense, right?
2) Or if I want straight lines, how do I do that without having 14 piece-wise functions?
3) Also, is there a way maybe to find the pattern of the slopes and make dY/dX equal to that pattern? That way I can work backwards using some calculus?

Thanks

 

[gb7nash]

You might want to take a look at this:

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

This is probably the easiest way of obtaining a single function to fit the points and derivatives. If you're allowing piecewise functions, you could take a look at spline interpolation. Cubic splines are pretty powerful, but you'll need some practice with it before you try.

 

[StillDumb]

Thanks, I'll take a look at those
P.s. - I don't care about the derivatives at all. Just the points and the return to zero in between each point

Here's an excel picture (but the lines don't go back to zero)
https://spreadsheets.google.com/spr...bE0za1ZnT2xKcmg3NGtaWGc&oid=1&zx=dx0qe04gnmz2