NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[ 157, 7]
-NotebookDataLength[ 8831, 250]
-NotebookOptionsPosition[ 8112, 221]
-NotebookOutlinePosition[ 8450, 236]
-CellTagsIndexPosition[ 8407, 233]
+NotebookDataLength[ 14247, 401]
+NotebookOptionsPosition[ 13118, 357]
+NotebookOutlinePosition[ 13454, 372]
+CellTagsIndexPosition[ 13411, 369]
WindowFrame->Normal*)
(* Beginning of Notebook Content *)
RowBox[{"\[Omega]_", ",", " ", "V0_"}], "]"}], " ", "=", " ",
RowBox[{"FourierTransform", "[",
RowBox[{
- RowBox[{"v", "[", "t", "]"}], ",", " ", "t", ",", " ", "\[Omega]"}],
- "]"}]}]], "Input",
+ RowBox[{"v", "[",
+ RowBox[{"t", ",", " ", "V0"}], "]"}], ",", " ", "t", ",", " ",
+ "\[Omega]"}], "]"}]}]], "Input",
CellChangeTimes->{{3.5523546214071712`*^9, 3.5523547025559893`*^9}, {
- 3.5523553152882023`*^9, 3.552355316326148*^9}}],
+ 3.5523553152882023`*^9, 3.552355316326148*^9}, {3.5523637265479307`*^9,
+ 3.55236372696416*^9}}],
Cell[BoxData[
RowBox[{
FractionBox["\[Pi]", "2"]], " ", "V0", " ",
RowBox[{"DiracDelta", "[", "\[Omega]", "]"}]}]}]], "Output",
CellChangeTimes->{{3.552354637903281*^9, 3.5523546565521603`*^9}, {
- 3.552354705534474*^9, 3.552354708319261*^9}, 3.552355316878035*^9}]
-}, Open ]],
-
-Cell[CellGroupData[{
-
-Cell[BoxData[
- RowBox[{"amplitude", " ", "=", " ",
- SuperscriptBox[
- RowBox[{"Abs", "[",
- RowBox[{
- RowBox[{"V", "[", "\[Omega]", "]"}], " ", "/.", " ",
- RowBox[{"V0", " ", "\[Rule]", " ", "1"}]}], "]"}], "2"]}]], "Input",
- CellChangeTimes->{{3.5523547568263407`*^9, 3.5523547725826674`*^9}}],
-
-Cell[BoxData[
- SuperscriptBox[
- RowBox[{"Abs", "[",
- RowBox[{
- RowBox[{"-",
- FractionBox["\[ImaginaryI]",
- RowBox[{
- SqrtBox[
- RowBox[{"2", " ", "\[Pi]"}]], " ", "\[Omega]"}]]}], "-",
- RowBox[{
- SqrtBox[
- FractionBox["\[Pi]", "2"]], " ",
- RowBox[{"DiracDelta", "[", "\[Omega]", "]"}]}]}], "]"}], "2"]], "Output",\
-
- CellChangeTimes->{{3.552354765629209*^9, 3.552354773172522*^9}}]
+ 3.552354705534474*^9, 3.552354708319261*^9}, 3.552355316878035*^9, {
+ 3.55236372229109*^9, 3.5523637274639397`*^9}}]
}, Open ]],
Cell[BoxData[
SuperscriptBox[
RowBox[{"(",
RowBox[{
- FractionBox[
- RowBox[{"-", "\[ImaginaryI]"}],
- RowBox[{"\[Omega]", " ", "c"}]], "+", " ",
+ RowBox[{"\[ImaginaryI]", " ", "\[Omega]", " ", "c"}], "+", " ",
FractionBox["1", "Ra"]}], ")"}],
RowBox[{"-", "1"}]], "+", "Rg"}]]}]], "Input",
CellChangeTimes->{{3.5523548800075397`*^9, 3.552354915946725*^9}, {
3.552354948404332*^9, 3.5523549491684923`*^9}, {3.552355018225143*^9,
3.5523550262754383`*^9}, {3.5523552038190727`*^9, 3.552355222703746*^9}, {
3.552355279891653*^9, 3.552355285419094*^9}, {3.55235535015308*^9,
- 3.552355350612905*^9}}],
+ 3.552355350612905*^9}, {3.552363701124979*^9, 3.552363703641261*^9}}],
Cell[CellGroupData[{
Cell[BoxData[
TagBox[
StyleBox[
- DynamicModuleBox[{$CellContext`c$$ = 1.*^-10, $CellContext`Ra$$ =
- 1, $CellContext`Rg$$ = 10000, $CellContext`V0$$ = -10, Typeset`show$$ =
+ DynamicModuleBox[{$CellContext`c$$ = 8.08*^-7, $CellContext`Ra$$ =
+ 1, $CellContext`Rg$$ = 10000., $CellContext`V0$$ = -10, Typeset`show$$ =
True, Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu",
Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ =
"\"untitled\"", Typeset`specs$$ = {{
Hold[$CellContext`c$$], 1.*^-10, 1.*^-6}, {
Hold[$CellContext`V0$$], -10, 0}}, Typeset`size$$ = {360., {99., 103.}},
Typeset`update$$ = 0, Typeset`initDone$$, Typeset`skipInitDone$$ =
- True, $CellContext`Rg$3664$$ = 0, $CellContext`Ra$3665$$ =
- 0, $CellContext`c$3666$$ = 0, $CellContext`V0$3667$$ = 0},
+ True, $CellContext`Rg$1179$$ = 0, $CellContext`Ra$1180$$ =
+ 0, $CellContext`c$1181$$ = 0, $CellContext`V0$1182$$ = 0},
DynamicBox[Manipulate`ManipulateBoxes[
1, StandardForm,
"Variables" :> {$CellContext`c$$ = 1.*^-10, $CellContext`Ra$$ =
1, $CellContext`Rg$$ = 10000, $CellContext`V0$$ = -10},
"ControllerVariables" :> {
- Hold[$CellContext`Rg$$, $CellContext`Rg$3664$$, 0],
- Hold[$CellContext`Ra$$, $CellContext`Ra$3665$$, 0],
- Hold[$CellContext`c$$, $CellContext`c$3666$$, 0],
- Hold[$CellContext`V0$$, $CellContext`V0$3667$$, 0]},
+ Hold[$CellContext`Rg$$, $CellContext`Rg$1179$$, 0],
+ Hold[$CellContext`Ra$$, $CellContext`Ra$1180$$, 0],
+ Hold[$CellContext`c$$, $CellContext`c$1181$$, 0],
+ Hold[$CellContext`V0$$, $CellContext`V0$1182$$, 0]},
"OtherVariables" :> {
Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
100000000}, {$CellContext`Ra$$, 1, 100000000}, {$CellContext`c$$,
1.*^-10, 1.*^-6}, {$CellContext`V0$$, -10, 0}}, "Options" :> {},
"DefaultOptions" :> {}],
- ImageSizeCache->{405., {181., 186.}},
+ ImageSizeCache->{405., {204., 209.}},
SingleEvaluation->True],
Deinitialization:>None,
DynamicModuleValues:>{},
CellChangeTimes->{{3.55235495848225*^9, 3.5523549840217457`*^9}, {
3.552355042834875*^9, 3.552355057810268*^9}, 3.552355132149538*^9, {
3.5523551849403133`*^9, 3.552355223898213*^9}, {3.552355265198854*^9,
- 3.552355297304193*^9}, {3.552355341762637*^9, 3.552355361439733*^9}}]
+ 3.552355297304193*^9}, {3.552355341762637*^9, 3.552355361439733*^9},
+ 3.552363706588172*^9}]
}, Open ]],
+Cell[CellGroupData[{
+
Cell[BoxData[
RowBox[{"InverseFourierTransform", "[",
RowBox[{
- RowBox[{"current", "[",
+ FractionBox[
+ RowBox[{"V", "[",
+ RowBox[{"\[Omega]", ",", " ", "V0"}], "]"}],
+ RowBox[{
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"\[ImaginaryI]", " ", "\[Omega]", " ", "c"}], "+", " ",
+ FractionBox["1", "Ra"]}], ")"}],
+ RowBox[{"-", "1"}]], "+", "Rg"}]], ",", " ", "\[Omega]", ",", " ",
+ "t"}], "]"}]], "Input",
+ CellChangeTimes->{{3.5523637982497053`*^9, 3.5523638062192183`*^9}}],
+
+Cell[BoxData["$Aborted"], "Output",
+ CellChangeTimes->{3.5523640098356323`*^9, 3.5523646452999907`*^9}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"FullSimplify", "[",
+ RowBox[{
+ SuperscriptBox[
+ RowBox[{"(",
+ RowBox[{
+ RowBox[{"\[ImaginaryI]", " ", "\[Omega]", " ", "c"}], "+", " ",
+ FractionBox["1", "Ra"]}], ")"}],
+ RowBox[{"-", "1"}]], " ", "\[Equal]"}], " ", "]"}]], "Input",
+ CellChangeTimes->{{3.552364654471057*^9, 3.552364756301162*^9}}],
+
+Cell[BoxData["True"], "Output",
+ CellChangeTimes->{
+ 3.552364656822824*^9, {3.552364728187964*^9, 3.552364752396307*^9}}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{
+ RowBox[{"FullSimplify", "[",
+ FractionBox[
+ RowBox[{"V", "[",
+ RowBox[{"\[Omega]", ",", " ", "V0"}], "]"}],
RowBox[{
- "\[Omega]", ",", " ", "V0", ",", " ", "Ra", ",", " ", "c", ",", " ",
- "Rg"}], "]"}], ",", " ", "\[Omega]", ",", " ", "t"}], "]"}]], "Input",
- CellChangeTimes->{{3.552355366383127*^9, 3.552355381350226*^9}}]
+ FractionBox["Ra",
+ RowBox[{"1", " ", "+", " ",
+ RowBox[{"\[ImaginaryI]", " ", "\[Omega]", " ", "c", " ", "Ra"}]}]],
+ " ", "+", " ", "Rg"}]], "]"}], " ", "/.", " ",
+ RowBox[{"Ra", "\[Rule]", "0"}]}]], "Input",
+ CellChangeTimes->{{3.552364758667733*^9, 3.552364769421089*^9}, {
+ 3.552364825262887*^9, 3.5523648524645557`*^9}, {3.5523649477202578`*^9,
+ 3.552364947904368*^9}, {3.552366305750093*^9, 3.552366307977755*^9}}],
+
+Cell[BoxData[
+ FractionBox[
+ RowBox[{
+ RowBox[{"-",
+ FractionBox[
+ RowBox[{"\[ImaginaryI]", " ", "V0"}],
+ RowBox[{
+ SqrtBox[
+ RowBox[{"2", " ", "\[Pi]"}]], " ", "\[Omega]"}]]}], "-",
+ RowBox[{
+ SqrtBox[
+ FractionBox["\[Pi]", "2"]], " ", "V0", " ",
+ RowBox[{"DiracDelta", "[", "\[Omega]", "]"}]}]}], "Rg"]], "Output",
+ CellChangeTimes->{{3.55236476528161*^9, 3.552364795048193*^9},
+ 3.5523648276341877`*^9, 3.552364948283778*^9, {3.5523663031716547`*^9,
+ 3.5523663083058147`*^9}}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"InverseFourierTransform", "[",
+ RowBox[{"%", ",", " ", "\[Omega]", ",", " ", "t"}], "]"}]], "Input",
+ CellChangeTimes->{{3.55236477078284*^9, 3.552364793658351*^9}}],
+
+Cell[BoxData[
+ RowBox[{"-",
+ FractionBox[
+ RowBox[{"V0", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+",
+ RowBox[{"Sign", "[", "t", "]"}]}], ")"}]}],
+ RowBox[{"2", " ", "Rg"}]]}]], "Output",
+ CellChangeTimes->{
+ 3.552364775961145*^9, {3.552364821257627*^9, 3.552364830039164*^9}, {
+ 3.552366283736989*^9, 3.5523663108687963`*^9}}]
+}, Open ]],
+
+Cell[CellGroupData[{
+
+Cell[BoxData[
+ RowBox[{"Manipulate", "[",
+ RowBox[{
+ RowBox[{"Plot", "[",
+ RowBox[{
+ RowBox[{"-",
+ FractionBox[
+ RowBox[{"V0", " ",
+ RowBox[{"(",
+ RowBox[{"1", "+",
+ RowBox[{"Sign", "[", "t", "]"}]}], ")"}]}],
+ RowBox[{"2", " ", "Rg"}]]}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"t", ",", " ", "0", ",", " ", "60"}], "}"}]}], "]"}], ",", " ",
+
+ RowBox[{"{",
+ RowBox[{"V0", ",", " ",
+ RowBox[{"-", "10"}], ",", " ", "0"}], "}"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"c", ",", " ", "0", ",", " ",
+ SuperscriptBox["1",
+ RowBox[{"-", "6"}]]}], "}"}], ",", " ",
+ RowBox[{"{",
+ RowBox[{"Rg", ",", " ", "1", ",", " ", "1000000"}], "}"}]}],
+ "]"}]], "Input",
+ CellChangeTimes->{{3.552364832845214*^9, 3.552364924046647*^9}, {
+ 3.552366317981595*^9, 3.5523663245642023`*^9}}],
+
+Cell[BoxData[
+ TagBox[
+ StyleBox[
+ DynamicModuleBox[{$CellContext`c$$ = 0, $CellContext`Rg$$ =
+ 1, $CellContext`V0$$ = -10, Typeset`show$$ = True,
+ Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu",
+ Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ =
+ "\"untitled\"", Typeset`specs$$ = {{
+ Hold[$CellContext`V0$$], -10, 0}, {
+ Hold[$CellContext`c$$], 0, 1}, {
+ Hold[$CellContext`Rg$$], 1, 1000000}}, Typeset`size$$ = {
+ 360., {113., 117.}}, Typeset`update$$ = 0, Typeset`initDone$$,
+ Typeset`skipInitDone$$ = True, $CellContext`V0$1512095$$ =
+ 0, $CellContext`c$1512096$$ = 0, $CellContext`Rg$1512097$$ = 0},
+ DynamicBox[Manipulate`ManipulateBoxes[
+ 1, StandardForm,
+ "Variables" :> {$CellContext`c$$ = 0, $CellContext`Rg$$ =
+ 1, $CellContext`V0$$ = -10}, "ControllerVariables" :> {
+ Hold[$CellContext`V0$$, $CellContext`V0$1512095$$, 0],
+ Hold[$CellContext`c$$, $CellContext`c$1512096$$, 0],
+ Hold[$CellContext`Rg$$, $CellContext`Rg$1512097$$, 0]},
+ "OtherVariables" :> {
+ Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$,
+ Typeset`animator$$, Typeset`animvar$$, Typeset`name$$,
+ Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
+ Typeset`skipInitDone$$}, "Body" :>
+ Plot[-($CellContext`V0$$ (1 + Sign[$CellContext`t])/(
+ 2 $CellContext`Rg$$)), {$CellContext`t, 0, 60}],
+ "Specifications" :> {{$CellContext`V0$$, -10, 0}, {$CellContext`c$$, 0,
+ 1}, {$CellContext`Rg$$, 1, 1000000}}, "Options" :> {},
+ "DefaultOptions" :> {}],
+ ImageSizeCache->{405., {182., 187.}},
+ SingleEvaluation->True],
+ Deinitialization:>None,
+ DynamicModuleValues:>{},
+ SynchronousInitialization->True,
+ UnsavedVariables:>{Typeset`initDone$$},
+ UntrackedVariables:>{Typeset`size$$}], "Manipulate",
+ Deployed->True,
+ StripOnInput->False],
+ Manipulate`InterpretManipulate[1]]], "Output",
+ CellChangeTimes->{{3.5523648997105494`*^9, 3.552364924935335*^9}, {
+ 3.552366312210638*^9, 3.552366325370653*^9}}]
+}, Open ]]
},
-WindowSize->{740, 605},
-WindowMargins->{{146, Automatic}, {Automatic, 28}},
+WindowSize->{1280, 725},
+WindowMargins->{{0, Automatic}, {Automatic, 0}},
FrontEndVersion->"8.0 for Linux x86 (64-bit) (November 14, 2010)",
StyleDefinitions->"Default.nb"
]
Cell[557, 20, 152, 3, 30, "Input"],
Cell[712, 25, 634, 17, 30, "Input"],
Cell[CellGroupData[{
-Cell[1371, 46, 375, 9, 30, "Input"],
-Cell[1749, 57, 465, 13, 58, "Output"]
+Cell[1371, 46, 458, 11, 30, "Input"],
+Cell[1832, 59, 516, 14, 58, "Output"]
}, Open ]],
+Cell[2363, 76, 130, 2, 30, "Input"],
+Cell[2496, 80, 855, 20, 56, "Input"],
Cell[CellGroupData[{
-Cell[2251, 75, 309, 7, 30, "Input"],
-Cell[2563, 84, 429, 14, 57, "Output"]
+Cell[3376, 104, 1130, 27, 55, "Input"],
+Cell[4509, 133, 2650, 50, 430, "Output"]
}, Open ]],
-Cell[3007, 101, 130, 2, 30, "Input"],
-Cell[3140, 105, 850, 22, 57, "Input"],
Cell[CellGroupData[{
-Cell[4015, 131, 1130, 27, 73, "Input"],
-Cell[5148, 160, 2622, 49, 384, "Output"]
+Cell[7196, 188, 512, 14, 56, "Input"],
+Cell[7711, 204, 103, 1, 30, "Output"]
}, Open ]],
-Cell[7785, 212, 323, 7, 30, "Input"]
+Cell[CellGroupData[{
+Cell[7851, 210, 349, 9, 47, "Input"],
+Cell[8203, 221, 122, 2, 30, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[8362, 228, 606, 14, 55, "Input"],
+Cell[8971, 244, 526, 15, 76, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[9534, 264, 191, 3, 30, "Input"],
+Cell[9728, 269, 345, 10, 50, "Output"]
+}, Open ]],
+Cell[CellGroupData[{
+Cell[10110, 284, 869, 26, 50, "Input"],
+Cell[10982, 312, 2120, 42, 386, "Output"]
+}, Open ]]
}
]
*)
(* End of internal cache information *)
-
git.ucc.asn.au / matches / honours.git / blobdiff
UCC git Repository :: git.ucc.asn.au