TITLE: Estimating parameters to damped harmonic oscillator model early in process
QUESTION [0 upvotes]: I am observing a process that I assume fits the model of a damped harmonic oscillator. The solution to the diff eq is $P(t) = A + B e^{-\alpha t} + C e^{-\beta t} \cos (\omega t - \phi)$, where $A, B, \alpha, C, \beta, \omega, \phi$ are parameters determined by experimental data. Given some complete data that fit the model, it is easy to estimate those parameters. If I am observing live data, and I believe that the process is beginning to behave like the d.h.o, can I estimate the solution parameters from just the first few data points? If so, how?

REPLY [0 votes]: In theory seven points will give enough data.  If the measurements are perfect, they will.  I suspect the solution process will be badly conditioned because certain pairs of parameters, particularly $B,C$ and $\alpha, \beta$ have almost the same effect.  It will be a nonlinear problem that can probably only be solved numerically.
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