Annoying problem with minimization

[aclark-3]

Hello.

I've written a program which finds the resonance frequencies of a recorder (using 2nd order Runge-Kutta integration) for various open and closed positions of the finger holes. Actually right now I am trying to get the same results in MathCad as in my earlier Excel program, so that I can easily move on to using complex quantities. I have attached the file.

I am pretty sure that the basic computations are correct, and one can skip over them. The problem is with the minimization. Things are very sensitive to the inital "guess" frequency (at the top of the program). If I am off by say about 50 Hertz I get nonsense. Furthermore the final frequency found drifts slightly as I change the guess frequency. It's also very sensitive to the CTOL.

The fundamental frequency for the hole configuration set right now is 353.4 Hz.  If I guess around 800 Hz and search for the 2nd harmonic, I sometimes get around 743.9 Hz, but if I change the guess a tad I might get 347.1 Hz.

Any help appreciated.

Regards, Al

[AlanStevens]

alton clark wrote:

The problem is with the minimization. Things are very sensitive to the inital "guess" frequency (at the top of the program). If I am off by say about 50 Hertz I get nonsense.

Plot P2 as a function of frequency to see why:

Alan

[aclark-3]

thanks Alan.

I realize that there are multiple harmonic solutions.

Is there some way that I can restrict the search for frequency so that it only includes one specific harmonic?

Al

[RichardJ]

Create a solve block with a constraint:

[AlanStevens]

Or use a solve block with Minerr and look for several at the same time!

Alan

[aclark-3]

Thanks much, Alan