Solution = 
      NDSolve[{y''[t] + Sin[y[t]] + 0.05*y'[t] - 
              0.7*Cos[0.5*t] == 0,  
          y[0] == 0,  y'[0] == 0.3}, y, {t, 0, 1000}, 
        MaxSteps  -> 11000]
Plot[Evaluate[y[t] /. %], {t, 0, 1000}]

y1[t_] := Evaluate[
          y[t] /. Solution][[1]]
y1prime[t_] := y1'[t]
y1[20]
y1prime[20]

ParametricPlot[{y1[t], y1prime[t]}, {t, 900, 1000}]

Solution = 
      NDSolve[{y''[t] + Sin[y[t]] + 0.05*y'[t] - 
              0.4*Cos[0.5*t] == 0,  
          y[0] == 0,  y'[0] == 0.3}, y, {t, 0, 1000}, 
        MaxSteps  -> 11000]
Plot[Evaluate[y[t] /. %], {t, 0, 1000}]

y2[t_] := Evaluate[
          y[t] /. Solution][[1]]
y2prime[t_] := y2'[t]

ParametricPlot[{y2[t], y2prime[t]}, {t, 900, 1000}]