Re: damped oscilations data fit

• To: mathgroup at smc.vnet.net
• Subject: [mg70576] Re: damped oscilations data fit
• From: Roger Bagula <rlbagula at sbcglobal.net>
• Date: Fri, 20 Oct 2006 05:21:39 -0400 (EDT)
• References: <eh4ntl\$7sb\$1@smc.vnet.net> <eh7931\$dig\$1@smc.vnet.net>

```Jens-Peer 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
>
>
>|
>
>
>
>
Jens-Peer 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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