(* Content-type: application/mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 6.0' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       145,          7]
NotebookDataLength[     52521,        983]
NotebookOptionsPosition[     51702,        950]
NotebookOutlinePosition[     52035,        965]
CellTagsIndexPosition[     51992,        962]
WindowFrame->Normal
ContainsDynamic->False*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[TextData[StyleBox["Resonance and exponentially decaying time signal",
 FontSize->16]], "Input",
 CellChangeTimes->{{3.549214693230056*^9, 3.549214708571841*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{
      RowBox[{"HeavisideTheta", "[", "t", "]"}], " ", 
      RowBox[{"Sin", "[", 
       RowBox[{"omega2", " ", "t"}], "]"}], " ", 
      RowBox[{"Exp", "[", 
       RowBox[{
        RowBox[{"-", "a"}], " ", "t"}], "]"}]}], "/.", 
     RowBox[{"omega2", "->", "1"}]}], "/.", 
    RowBox[{"a", "->", "0.2"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"t", ",", 
     RowBox[{"-", "10"}], ",", "30"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.549214938890608*^9, 3.549214989392045*^9}}],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJxEl3c8lu8b90kkZUvZe+95c4fzKKKhMioNUVYSEbKzKtkhsjKSJDt71SlE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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.549214955184234*^9, 3.549214990664433*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{
  RowBox[{"f", "[", "omega_", "]"}], "=", 
  RowBox[{"FourierTransform", "[", 
   RowBox[{
    RowBox[{
     RowBox[{"HeavisideTheta", "[", "t", "]"}], " ", 
     RowBox[{"Sin", "[", 
      RowBox[{"omega2", " ", "t"}], "]"}], " ", 
     RowBox[{"Exp", "[", 
      RowBox[{
       RowBox[{"-", "a"}], " ", "t"}], "]"}]}], ",", "t", ",", "omega"}], 
   "]"}]}]], "Input",
 CellChangeTimes->{{3.549213864751908*^9, 3.549214028091881*^9}, {
  3.549214101296824*^9, 3.549214102125275*^9}, {3.54921434155936*^9, 
  3.54921447085677*^9}},
 FormatType->"InputForm"],

Cell[BoxData[
 FractionBox["omega2", 
  RowBox[{
   RowBox[{"(", 
    RowBox[{
     SuperscriptBox["a", "2"], "-", 
     RowBox[{"2", " ", "\[ImaginaryI]", " ", "a", " ", "omega"}], "-", 
     SuperscriptBox["omega", "2"], "+", 
     SuperscriptBox["omega2", "2"]}], ")"}], " ", 
   SqrtBox[
    RowBox[{"2", " ", "\[Pi]"}]]}]]], "Output",
 CellChangeTimes->{{3.549213875256266*^9, 3.549213996218433*^9}, 
   3.549214029047082*^9, 3.549214102735999*^9, {3.549214352404164*^9, 
   3.549214472226103*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Plot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"Abs", "[", 
      RowBox[{"f", "[", "omega", "]"}], "]"}], "/.", 
     RowBox[{"omega2", "->", "1"}]}], "/.", 
    RowBox[{"a", "->", "0.2"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"omega", ",", "0", ",", "10"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.549214032277017*^9, 3.549214113080515*^9}, {
  3.549214157855267*^9, 3.549214165912061*^9}, {3.549214475264947*^9, 
  3.549214540223014*^9}, {3.549214658079826*^9, 3.54921468285677*^9}, {
  3.549214889875478*^9, 3.549214902027063*^9}},
 FormatType->"InputForm"],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwV1nc0198fB3B7htCQhIoU0f6WqOe7RBlJIpIoIyMJRURSKhEZEdmEKGTv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     "]]}},
  AspectRatio->NCache[GoldenRatio^(-1), 0.6180339887498948],
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.549214052834764*^9, 3.549214113794382*^9}, {
  3.549214158442952*^9, 3.549214166764132*^9}, {3.549214483658018*^9, 
  3.549214540773686*^9}, {3.549214658935988*^9, 3.549214683313603*^9}, {
  3.549214890406605*^9, 3.549214902601911*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ParametricPlot", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Re", "[", 
        RowBox[{"f", "[", "omega", "]"}], "]"}], ",", 
       RowBox[{"Im", "[", 
        RowBox[{"f", "[", "omega", "]"}], "]"}]}], "}"}], "/.", 
     RowBox[{"omega2", "->", "1"}]}], "/.", 
    RowBox[{"a", "->", "0.2"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"omega", ",", "0", ",", "10"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.54921454364286*^9, 3.549214648316341*^9}, {
  3.549214885400187*^9, 3.549214907800165*^9}},
 FormatType->"InputForm"],

Cell[BoxData[
 GraphicsBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], LineBox[CompressedData["
1:eJwt13c81d//AHAjIisjm0+yCVFKGi9Z2aEhFCVkRFYoySwSUrKzkx3JFke2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     "]]}},
  Axes->True,
  AxesOrigin->{0, 0},
  PlotRange->{All, All},
  PlotRangeClipping->True,
  PlotRangePadding->{Automatic, Automatic}]], "Output",
 CellChangeTimes->{{3.549214580625781*^9, 3.549214649234666*^9}, 
   3.549214779772841*^9, {3.549214886176284*^9, 3.549214908586057*^9}}]
}, Open  ]],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"ParametricPlot3D", "[", 
  RowBox[{
   RowBox[{
    RowBox[{
     RowBox[{"{", 
      RowBox[{
       RowBox[{"Re", "[", 
        RowBox[{"f", "[", "omega", "]"}], "]"}], ",", 
       RowBox[{"Im", "[", 
        RowBox[{"f", "[", "omega", "]"}], "]"}], ",", 
       RowBox[{"Abs", "[", 
        RowBox[{"f", "[", "omega", "]"}], "]"}]}], "}"}], "/.", 
     RowBox[{"omega2", "->", "1"}]}], "/.", 
    RowBox[{"a", "->", "0.2"}]}], ",", 
   RowBox[{"{", 
    RowBox[{"omega", ",", "0", ",", "10"}], "}"}], ",", 
   RowBox[{"PlotRange", "->", "All"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.549214785851823*^9, 3.549214879509998*^9}, {
  3.549214913431356*^9, 3.549214913729406*^9}},
 FormatType->"InputForm"],

Cell[BoxData[
 Graphics3DBox[{{}, {}, 
   {Hue[0.67, 0.6, 0.6], Line3DBox[CompressedData["
1:eJwt12k0VV8fB3BJI2VokFRSSAMqDRS+iDInDZSpkPlvylBIhlAkSRIqIlII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     "]]}},
  Axes->True,
  ImageSize->{360., 398.2723423357919},
  PlotRange->{All, All, All},
  PlotRangePadding->{Automatic, Automatic, Automatic},
  ViewPoint->{-2.953198693107498, -1.6507336022882788`, 
   0.060795175010232926`},
  ViewVertical->{-0.5518682084667668, -0.31974114862461006`, 
   0.792518248121907}]], "Output",
 CellChangeTimes->{{3.549214814687163*^9, 3.549214880289936*^9}, 
   3.549214914363157*^9}]
}, Open  ]]
},
WindowSize->{927, 623},
WindowMargins->{{150, Automatic}, {Automatic, 52}},
FrontEndVersion->"6.0 for Linux x86 (32-bit) (June 2, 2008)",
StyleDefinitions->"Default.nb"
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[568, 21, 166, 2, 36, "Input"],
Cell[CellGroupData[{
Cell[759, 27, 618, 18, 55, "Input"],
Cell[1380, 47, 23157, 384, 237, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[24574, 436, 582, 16, 32, "Input"],
Cell[25159, 454, 503, 13, 53, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[25699, 472, 653, 16, 32, "Input"],
Cell[26355, 490, 8047, 136, 242, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[34439, 631, 647, 18, 55, "Input"],
Cell[35089, 651, 7853, 133, 378, "Output"]
}, Open  ]],
Cell[CellGroupData[{
Cell[42979, 789, 733, 20, 55, "Input"],
Cell[43715, 811, 7971, 136, 413, "Output"]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
