Clear[g]; 
    g[t_] := Plot[(E^(-t)) Sin[x], {x, 0, π}, 
        AspectRatio -> Automatic, PlotStyle -> Hue[0.0], 
        AxesLabel -> {x, u}, Ticks -> {{0, π}, {0, 1}}, 
        PlotRange -> {{0, π}, {0, 1}}, PlotPoints -> 600]; 
    Do[g[t], {t, 0, 3, 0.05}]