tmax = 5

v = 2

sol2  =  
      NDSolve[{x'[t]  ==  
            y[t],  y'[t] ==  -4*Sin[x[t]],  x[0] == 0, 
          y[0] == v},  {x[t], y[t]}, {t, 0, tmax}]

v2plot  = 
      Plot[Evaluate[x[t]]  /. sol2,  {t, 0, tmax},  
        PlotStyle  ->  {{RGBColor[1,  0, 0]}}]

v = 3.999

sol3  =  
      NDSolve[{x'[t]  ==  
            y[t],  y'[t] ==  -4*Sin[x[t]],  x[0] == 0, 
          y[0] == v},  {x[t], y[t]}, {t, 0, tmax}]

v3plot  = 
      Plot[Evaluate[x[t]]  /. sol3,  {t, 0, tmax},  
        PlotStyle  ->  {{RGBColor[0,  0, 1]}}]

v = 5

sol5  =  
      NDSolve[{x'[t]  ==  
            y[t],  y'[t] ==  -4*Sin[x[t]],  x[0] == 0, 
          y[0] == v},  {x[t], y[t]}, {t, 0, tmax}]

v5plot  = 
      Plot[Evaluate[x[t]]  /. sol5,  {t, 0, tmax},  
        PlotStyle  ->  {{RGBColor[0,  1, 0]}}]

Show[v2plot, v3plot, v5plot]