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Re: damped oscilations data fit
 To: mathgroup at smc.vnet.net
 Subject: [mg70616] Re: damped oscilations data fit
 From: "JensPeer Kuska" <kuska at informatik.unileipzig.de>
 Date: Sat, 21 Oct 2006 05:14:06 0400 (EDT)
 Organization: Uni Leipzig
 References: <eh4ntl$7sb$1@smc.vnet.net> <eh7931$dig$1@smc.vnet.net> <eha4vs$b1b$1@smc.vnet.net>
Hi Roger,
the physical time dependence of a damped
oscillator
*is*
Exp[lambda*t]*(c1*Sin[omega*t]+c2*Cos[omega*t])
and I would like to see what differential
equation/force law
you are using to get
model=a*Exp[w^2*t^2]+b*Sin[w*t]+c
And even when you model perfectly fit to the data,
I would prefer
a model that can justifyed by physical laws and
fit not so well...
Regards
Jens
"Roger Bagula" <rlbagula at sbcglobal.net> schrieb im
Newsbeitrag news:eha4vs$b1b$1 at smc.vnet.net...
 JensPeer Kuska wrote:

 >Hi,
 >
 >model = Exp[l*t]*Sin[w*t + phi] + c;
 >ff = FindFit[N[data], model, {{l, 1/1000}, {w,
 >1/400}, {phi, 0}, {c, 60}}, t]
 >
 >Plot[Evaluate[model /. ff], {t, 0, 1014},
 >PlotRange > All,
 >Epilog > {Point /@ data}]
 >
 >Regards
 > Jens
 >
 >
 >
 >
 >
 >
 >
 JensPeer Kuska,
 Your mechanics work fine here, but a better
model seems to be an
 Gaussian decay
 instead of an exponential one:
 model=a*Exp[w^2*t^2]+b*Sin[w*t]+c
 Roger
 a = {{0, 54}, {120, 56.5}, {230, 56}, {305, 54},
{340,
 53}, {360, 52.7}, {378, 52.5}, {
 405, 52.5}, {443, 53}, {480, 53.5}, {510,
54}, {540, 54.7}, {570,
 54.4}, {602, 56}, {643, 56.5}, {660, 56.5}, {
 685, 56.25}, {706, 56}, {727, 55.25}, {743,
55.5}, {756, 55.25}, {775,
 55}, {787, 54.75}, {799, 54.5}, {814,
54.25}, {828, 54}, {845,
 53.75}, {
 858, 53.5}, {877, 53.25}, {894, 53}, {923,
52}, {951,
 53}, {983, 53.5}, {1014, 54}}
 g = ListPlot[a, PlotJoined > True]
 y[x_] = Fit[a, {1, Exp[x^2/89^2], Sin[x/89]},
x]
 g1 = Plot[y[x], {x, 0, 1050}]
 Show[{g, g1}]

 data = {{0, 54}, {120, 56.5}, {230, 56}, {305,
 54}, {340, 53}, {360, 52.7}, {378, 52.5},
{405, 52.5}, {
 443, 53}, {480, 53.5}, {510, 54}, {540,
54.7}, {
 570, 54.4}, {602, 56}, {643, 56.5}, {660,
56.5}, {685, 56.25}, {
 706, 56}, {
 727, 55.25}, {743, 55.5}, {756, 55.25}, {775,
55}, {787, 54.75}, {799, \
 54.5}, {814, 54.25}, {828, 54}, {845, 53.75},
{858,
 53.5}, {877, 53.25}, {894, 53}, {923,
 52}, {951, 53}, {983, 53.5}, {1014, 54}}
 model = Exp[(w*t + phi)^2] + l*Sin[w*t + phi] +
c;
 ff = FindFit[N[data], model, {{l, 1/1000}, {w,
 1/400}, {phi, 0}, {c, 60}}, t]
 g1 = Plot[Evaluate[model /. ff], {t, 0, 1014},
 Epilog > {Point /@ data}]
 g = ListPlot[data, PlotJoined > True]
 Show[{g, g1}]

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