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fitting critically damped simple harmonic oscillator

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Four-parameter fit to the equation A*(1 + t/T2).*exp(-t/T1) + offset

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[A, T1, T2, offset, Ssq] = fit_critical_damping( t, y, options )
fitting critically damped oscillations to the equation
y(t) = A (1 + t/T2) exp( -t/T1 ) + offset
where A is the amplitude, T1 is a time constant, T2 is the decay time, along with
the offest. Ssq is the sum of residuals (i.e. fitting error).

options are 'notify' to show progress and 'plot' to give a plot
you can also supply a guess or series of guesses via a row vector or
matrix, m, where size( m, 2 ) = 4 (i.e. there are four columns);

if you just run program without arguments it will do an example

examples are
fit_critical_damping( t, y, 'notify', 'plot')
[A, T1, T2, offset, Ssq] = fit_critical_damping( t, y, [1 2 3 4] )

Note: this script uses LMFnlsq from MATLAB central file exchange
sak@wpi.edu 2/8/12

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MATLAB 6.5 (R13)

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