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    <p>This should do it.</p> <pre><code>m = 10; c = 2; k = 5; F = 12; fun[f_?NumericQ] := Module[ {x, t}, First[x /. NDSolve[ {m*x''[t] + c*x'[t] + (k*Sin[2*Pi*f*t])*x[t] == F*Sin[2*Pi*f*t], x[0] == 0, x'[0] == 0}, x, {t, 0, 30} ] ] ] ContourPlot[fun[f][t], {f, 0, 5}, {t, 0, 30}] </code></pre> <p>Important points:</p> <ul> <li><p>The pattern _?NumericQ prevents <code>fun</code> from being evaluated for symbolc arguments (think <code>fun[a]</code>), and causing <code>NDSolve::nlnum</code> errors.</p></li> <li><p>Since <code>NDSolve</code> doesn't appear to localize its function variable (<code>t</code>), we needed to do this manually using <code>Module</code> to prevent conflict between the <code>t</code> used in <code>NDSolve</code> and the one used in <code>ContourPlot</code>. (You could use a differently named variable in <code>ContourPlot</code>, but I think it was important to point out this caveat.)</p></li> </ul> <hr> <p>For a significant speedup in plotting, you can use <a href="http://en.wikipedia.org/wiki/Memoization" rel="nofollow">memoization</a>, as pointed out by Mr. Wizard.</p> <pre><code>Clear[funMemo] (* very important!! *) funMemo[f_?NumericQ] := funMemo[f] = Module[{x, t}, First[x /. NDSolve[{m*x''[t] + c*x'[t] + (k*Sin[2*Pi*f*t])*x[t] == F*Sin[2*Pi*f*t], x[0] == 0, x'[0] == 0}, x, {t, 0, 30}]]] ContourPlot[funMemo[f][t], {f, 0, 5}, {t, 0, 30}] (* much faster than with fun *) </code></pre> <hr> <p>If you're feeling adventurous, and willing to explore Mathematica a bit more deeply, you can further improve this by limiting the amount of memory the cached definitions are allowed to use, <a href="http://web.ift.uib.no/~szhorvat/mmatricks.php" rel="nofollow">as I described here</a>.</p> <p>Let's define a helper function for enabling memoization:</p> <pre><code>SetAttributes[memo, HoldAll] SetAttributes[memoStore, HoldFirst] SetAttributes[memoVals, HoldFirst] memoVals[_] = {}; memoStore[f_, x_] := With[{vals = memoVals[f]}, If[Length[vals] &gt; 100, f /: memoStore[f, First[vals]] =.; memoVals[f] ^= Append[Rest[memoVals[f]], x], memoVals[f] ^= Append[memoVals[f], x]]; f /: memoStore[f, x] = f[x]] memo[f_Symbol][x_?NumericQ] := memoStore[f, x] </code></pre> <p>Then using the original, non-memoized <code>fun</code> function, plot as</p> <pre><code>ContourPlot[memo[fun][f][t], {f, 0, 5}, {t, 0, 30}] </code></pre>
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    3. CONow it works, but I think you will want to add memoization.
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