Here's an example of two curves that are simultaneously animated by MATHEMATICA.
Table[
Show[
{ParametricPlot[ {{Cos[3t], Sin[4t]}, {Sin[2t], Cos[5t]}}, {t, 0, s},
AspectRatio -> 1, PlotRange -> {{-1.2, 1.2}, {-1.2, 1.2}},
PlotStyle -> {{Hue[0], Thickness[.007]}, {Hue[.7], Thickness[.007]}},
Background -> RGBColor[0.67, 1, 0.75]],
Graphics[{PointSize[.025], Hue[0], Point[{Cos[3s], Sin[4s]}]}] ,
Graphics[{PointSize[.025], Hue[.7], Point[{Sin[2s], Cos[5s]}]} ]},
Background -> RGBColor[0.67, 1, 0.75]],
{s, 0, 2Pi, 2Pi/36}]
will result in the animation

URL: http://math.ou.edu/~amiller/math/pplot2.htm
November, 1999