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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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