Question: how to animate like weather diagram?

with(DEtools):
rho := 0.1;
w0 := 2;
sys := {diff(x(t),t) = y(t),diff(y(t),t) = -2*rho*y - w0^2*x};
DEplot(sys, [x(t), y(t)], t = 0 .. 12, [[x(0) = 1, y(0) = 0]]);

i use flow above, would like to plot a circle move from right hand side to left hand side

and see how a circle influence the flow diagram in animation like weather diagram

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