Please see this:
sol = {E^(-0.035 t) (1.085 Cos[0.31 t] + 2.95 Sin[0.31 t]), -1.1 Sin[
0.0 - 0.1 t]}
Now I plot this, one time with Chop and another without Chop. Colors go away
Plot[sol, {t, 0, 10}, PlotStyle -> {Red, Blue}]
Plot[Chop@sol, {t, 0, 10}, PlotStyle -> {Red, Blue}]