plot = Manipulate[ParametricPlot[{r Cos[x], r Sin[x]}, {x, 1, m}, {r, 0, k},
Mesh -> Full,
PlotRange -> {{-2, 2}, {-2, 2}}],
{m, 0, 20 Pi}, {k, 1, 3}]

Row[{plot, plot}]

Change the sliders then re-evaluate Row[{plot, plot}]
. Both should reset to their initial state.