title: Need help with solving differential equation and plotting velocity as a function of forcing term magnitude
body: <p>I needed some help with plotting a velocity vs forcing term diagram for a chaotic oscillator on mathematica.</p>
  
  <p>Basically, I have to solve the following differential equation</p>
  
  <pre><code>x''[t] + b x'[t] - x[t] + x[t]^3 - f Cos[w t] == 0, x'[0] == 0, 
   x[0] == 0
  </code></pre>
  
  <p>and plot the velocity of my solution for times in the interval [0,1000] in increments of 2*Pi
  for different values of f.</p>
  
  <p>That is, for each f in the interval [0,2] (in increments of .05), I will have approximately 150 velocity points, and I must plot all of these points on one graph.</p>
  
  <p>I though about using a do loop and came up with something like</p>
  
  <pre><code>Remove["Global`*"]
  
  b = .1;
  w = 1;
  Period = 1;
  tstep = 2 Pi/Period;
  
  Do[{Do[{data = 
       Table[Flatten[
         Evaluate[{f, 
           x'[t] /. 
            NDSolve[{x''[t] + b x'[t] - x[t] + x[t]^3 - f Cos[w t] == 0,
               x'[0] == 0, x[0] == 0}, x[t], {t, 0, 1000}, 
             MaxSteps -&gt; 59999]}]], {t, 0, 1000, tstep}]}, {t, 0, 1000, 
      1}]}, {f, 0, 2, .1}]
  </code></pre>
  
  <p>but had no luck.</p>
  
  <p>How can I do this?</p>