a = 0.01
V = a ((x^2) + (y^2)) - 20 Cos[(x/2)] - 20 Cos[(y/4)]
ContourPlot[V, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 60]
Plot3D[V, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 30]
t = 40
Vt = 
      a ((x^2) + (y^2)) + 4 t - 
        20 Cos[(x/2)] (E^(-(t/4))) - 
        20 Cos[(y/4)] (E^(-(t/16)))
ContourPlot[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 60]
Plot3D[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 30]
t = 20
Vt = 
      a ((x^2) + (y^2)) + 4 t - 
        20 Cos[(x/2)] (E^(-(t/4))) - 
        20 Cos[(y/4)] (E^(-(t/16)))
ContourPlot[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 60]
Plot3D[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 30]
t = 10
Vt = 
      a ((x^2) + (y^2)) + 4 t - 
        20 Cos[(x/2)] (E^(-(t/4))) - 
        20 Cos[(y/4)] (E^(-(t/16)))
ContourPlot[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 60]
Plot3D[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 30]
t = 5
Vt = 
      a ((x^2) + (y^2)) + 4 t - 
        20 Cos[(x/2)] (E^(-(t/4))) - 
        20 Cos[(y/4)] (E^(-(t/16)))
ContourPlot[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 60]
Plot3D[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 30]
t = 0
Vt = 
      a ((x^2) + (y^2)) + 4 t - 
        20 Cos[(x/2)] (E^(-(t/4))) - 
        20 Cos[(y/4)] (E^(-(t/16)))
ContourPlot[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 60]
Plot3D[Vt, {x, -50, 50}, {y, -50, 50}, 
      PlotPoints -> 30]