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Re: damped oscilations data fit

• To: mathgroup at smc.vnet.net
• Subject: [mg70585] Re: damped oscilations data fit
• From: "Ray Koopman" <koopman at sfu.ca>
• Date: Fri, 20 Oct 2006 05:21:54 -0400 (EDT)
• References: <eh4ntl$7sb$1@smc.vnet.net><eh7aqc$e8r$1@smc.vnet.net>

Ray Koopman wrote:
> [...] guess at the form of the function:
>    y = a + b*Sin[t/c]*Exp[-t/d]
> [...]

y = a + (b1*Sin[t/c] + b2*Cos[t/c])*Exp[-t/d]  gives a better fit:
the root-mean-square residual is .291, compared to .327 for the
sine-only model. The difference is statistically significant
(assuming the residuals are i.i.d. normal), and the plot looks
better. The parameter estimates are
a = 54.5192, b1 = 2.22174, b2 = -0.60541, c = 82.0552, d = 2661.24