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MathGroup Archive 2006

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Re: damped oscilations data fit

  • To: mathgroup at smc.vnet.net
  • Subject: [mg70547] Re: damped oscilations data fit
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Thu, 19 Oct 2006 03:22:22 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <eh4ntl$7sb$1@smc.vnet.net>

Miroslav Hýža wrote:
> hello,
> I have one question about data manipulation in mathematica.
> I've got set of experimental data. Data describe damped oscillation. My question is following:
> 
> How can I fit these data? 
> I would like to get formula of function which will approximately describe my data and plot this function.
> 
> my data list:
> {{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}}
> 
> Have anyone an idea?
> I'm mathematica beginner therefore I'll be grateful for any suggestion.
> Thanks
> <<mira
> 
Hi Mira,

Have a look at the function Fit [1]. For instance, the online help and 
the following expressions should help you started.

points = {{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}};

plotpoints = ListPlot[points, PlotStyle -> PointSize[0.02]];
Fit[points, {1, Sin[x/80], Cos[x/80]}, x]
plotline = Plot[%, {x, Min[points[[All,1]]], Max[points[[All,1]]]}];
Show[plotpoints, plotline];

Regards,
Jean-Marc

1. http://documents.wolfram.com/mathematica/functions/Fit


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