Finding parameter to fit known eq. to 3 points?

To all,

I am trying to see if one can find a parameter required to fit a known equation to a set of data points. See attached.

I have an equation Q(w,wn,zeta) and would like to see if it 's possible to find the value of zeta required to fit the Q() for a given data set

Test 1:

For a given range of w values, a value of wm and zeta = 0.04, I calculated the Q value, allocated them to a table to “mimic” a data set (not important but it follows how data is provided. I am trying to work “backward” by trying to find the zeta value required to fits Q at the max value. (Obviously mcad must predict zeta  =0.04 !)

I have set up ‘test 1’ as a root() but nothing is return

Test 2:

  Use a subset of a known data set and see if one can find the zeta value required to fit Q() passing through 3 points of that subset

I know that must people will say that I am tackling the problem the wrong way but I have to start somewhere and that why I am looking for advice

Any pointers by the more mathematically inclined out there would be much appreciated

Thanks

Regards