x0 = 0;
y0 = 0;
w = 1;
other parameters  =  ?;
ndrive  = 1000;
tstart = 0;
tend = ndrive*2*Pi/w;

sol = 
      NDSolve[{x'[t] == 
            y[t], 
           y'[t] == 
            fill this in, 
           y[
              0] == y0, 
          x[0] == x0}, 
             {y, 
          x}, {t, tstart, tend}, MaxSteps -> 400000]

Plot[x[t] /. sol,  {t,  1100,  1150}];

ParametricPlot[{x[t], y[t]} /. sol, {t, 1100, 1200}];

\(\(\( (*\ 
      Poincare\ Section\ *) \)\(
\)\(
\)\(\(phase\  = \ \(-Pi\)/2;\)

    \(py\  = \ Table[0, {i, 20, ndrive}];\)

    \(Do[{py[\([i]\)]\  = \ 
            y[\((\((i + 20)\) + \ \ phase\ )\)*2\ Pi/w\ ] /. 
              sol[\([1]\)]}, {i, ndrive - 21}];\)\)\)\)

py;

px  =  Table[0, {i, 20, ndrive}];
Do[{px[[i]]  =  
          Mod[x[((i + 20)  +  phase )*2 Pi/w ] +  Pi, 
                2 Pi]  -  Pi /. sol[[1]]}, {i, 1, 
        ndrive - 21}]

px;

ListPlot[Transpose[{px, py}], PlotRange -> All, 
        PlotStyle -> PointSize[ .02]];