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First \ the analytic solution of the linear case\ \>", "Text", CellChangeTimes->{{3.4676616795973306`*^9, 3.467661681063712*^9}, { 3.4681545073136578`*^9, 3.4681545715076575`*^9}}], Cell[BoxData[ RowBox[{"Clear", "[", "f", "]"}]], "Input", CellChangeTimes->{{3.4676632536397843`*^9, 3.467663258272925*^9}}], Cell[BoxData[ RowBox[{"DSolve", "[", RowBox[{ RowBox[{ RowBox[{ RowBox[{ RowBox[{"x", "''"}], "[", "t", "]"}], "+", RowBox[{"2", " ", "\[Lambda]", " ", RowBox[{ RowBox[{"x", "'"}], "[", "t", "]"}]}], "+", RowBox[{ SubsuperscriptBox["\[Omega]", "0", "2"], RowBox[{"x", "[", "t", "]"}]}]}], "==", RowBox[{ FractionBox["f", "m"], RowBox[{"Cos", "[", RowBox[{ SubscriptBox["\[Omega]", "D"], "t"}], "]"}]}]}], ",", RowBox[{"x", "[", "t", "]"}], ",", "t"}], "]"}]], "Input", CellChangeTimes->{{3.4676628481697826`*^9, 3.467663007584139*^9}}], Cell["\<\ Now consider the nonlinear case and swept the driving frequency for chosen \ values of the other parameters. 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