Perturbation Theory Example

epsilon = 0.3; Plot[{1/Sqrt[1 - epsilon^2] Exp[-epsilon t] Sin[
    Sqrt[1 - epsilon^2] t],
  Exp[-epsilon t] Sin[t]}, {t, 0, 20}, 
 PlotLegends -> {"Exact", "Pert"}, PlotRange -> {-0.5, 0.8}]