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8180877
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2011-11-18T10:22:15.730
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2011-11-18T10:49:48.380
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2011-11-18T10:49:48.380
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Here goes a solution. <pre><code>m = 10; c = 2; k = 5; F = 12; NumberOfDiscrit$f = 20;(* Number of points you want to divide 0<=f<=5*) NumberOfDiscrit$t = 100;(* Number of points you want to divide 0<=t<=30 *) fValues = Range[0., 5., 5./(NumberOfDiscrit$f - 1)]; tValues = Range[0., 30., 30./(NumberOfDiscrit$t - 1)]; res = Map[(x /. First@First@ NDSolve[{m*x''[t] + c*x'[t] + (k*Sin[2*Pi*#*t])*x[t] == F*Sin[2*Pi*#*t], x[0] == 0, x'[0] == 0}, x, {t, 0, 30}]) &, fValues]; AllDat = Map[(#@tValues) &, res]; InterpolationDat = Flatten[Table[ Transpose@{tValues, Table[fValues[[j]], {i, 1, NumberOfDiscrit$t}], AllDat[[j]]}, {j, 1, NumberOfDiscrit$f}], 1]; Final3DFunction = Interpolation[InterpolationDat]; Plot3D[Final3DFunction[t, f], {t, 0, 30}, {f, 0, 5}, PlotRange -> All, PlotPoints -> 60, MaxRecursion -> 3, Mesh -> None] </code></pre> <img src="https://i.stack.imgur.com/wrkK8.png" alt="enter image description here"> You can use <code>Manipulate</code> to dynamically change some of the parameters. By the way the above 3D picture may be misleading if one takes <code>f</code> as a continuous variable in <code>u(t,f)</code>. You should note that the numerical solution seems to blow up for asymptotic values of <code>t>>30</code>. See the picture below. <img src="https://i.stack.imgur.com/pv9km.png" alt="enter image description here"> <img src="https://i.stack.imgur.com/Oo6pU.png" alt="enter image description here"> Hope this helps you out.
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