Damped oscillation fit We have some measurement data like this:  
 
The expected behavior of the data is a damped oscillation:
$$y=a e^{d*t} cos(\omega t+\phi) + k$$
Where:
$t$ Current time
$y$ Current deflection  
$a$ Amplitude
$d$ Damping factor
$\omega$ Angluar velocity
$\phi$ Phase shift
$k$ Offset
The task is to fit the 5 parameters to match the real data.
Our current approch does the following:
- Find start values for all 5 parameters
- Place the values into a system of equations
- Iterate until the error gets below a given value
In most cases this works well. But in some cases it fails (breaking after 100 iterations). Now there are two possible options:
1) Suppose that the data is 'too bad' and give up
2) Find a better solution
Does anyone have a idea of different ways to solve this?

Your data obviously doesn't fit your trial equation.  It appears to be two oscillations beating with dissipation.  Could be two coupled oscillators?  Try fitting to the solution of the coupled diff. equations.  A.P. French's "Vibrations and Waves" does this at the beginner's level well.  I've done it both numerically and experimentally using a spring loaded cart as the support of a pendulum.  This prob. is solved by AP French [MIT internet course --not the text] linearized, and exactly by Cooper and Pellegrini in "Modern Analytic Mechanics".  
bc
