Henrik and Rohit, Thanks a lot.
Most likely because of existing conflicting symbol definitions. Try ClearAll[r] or quit the kernel.
ClearAll[r]
Georges, try:
r[t_] := 5 + Sin[20 t]; curves = ParametricPlot[r[t] {Cos[t], Sin[t]}, {t, 0, 2 Pi}]; Animate[Show[curves, Graphics[{PointSize[Large], Point[r[t] {Cos[t], Sin[t]}]}]], {t, 0, 2 Pi}]
