(* 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[ 25400, 635] NotebookOptionsPosition[ 24633, 609] NotebookOutlinePosition[ 24972, 624] CellTagsIndexPosition[ 24929, 621] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ StyleBox["Energy\n", "Title"], "JT 25 Jan 2010", StyleBox["\[LineSeparator]", "Title"], "CMD-shift-F gives help on selection (same as apple-shift-F)\n", StyleBox["Mathematica", FontSlant->"Italic"], " needs esc(ii) esc to recognize \"i\" as sqrt(-1). Capital I aslo works. \ This shows as a black i. If it is the variable i, it is blue.\nTo define a \ function, need f[x_,y_] :=, not just =. Another way is f=Function[{x,y},x+y] \ and then ask for f[1,2] or f[x,y].\n" }], "Text", CellChangeTimes->{{3.473220102244772*^9, 3.473220125187995*^9}, { 3.473442172676305*^9, 3.473442172967043*^9}, {3.4734493298480043`*^9, 3.473449361622698*^9}, {3.473472427704431*^9, 3.4734724670541143`*^9}, { 3.4734725798321466`*^9, 3.473472620403522*^9}, {3.473472719859336*^9, 3.473472730532486*^9}, {3.4734761480032578`*^9, 3.473476199902961*^9}, { 3.53747591696665*^9, 3.537475918341894*^9}, {3.5374763209338207`*^9, 3.537476321865697*^9}, {3.551555194179792*^9, 3.551555195010524*^9}}], Cell[TextData[StyleBox["Traveling wave", "Subtitle"]], "Text", CellChangeTimes->{{3.473472482411351*^9, 3.4734725034239473`*^9}, { 3.473472569742597*^9, 3.4734725709423923`*^9}, {3.474643702935645*^9, 3.474643705501945*^9}, {3.537476333361525*^9, 3.5374763339129744`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"\[Phi]", "[", RowBox[{"x_", ",", "t_"}], "]"}], ":=", RowBox[{"Cos", "[", RowBox[{ RowBox[{"\[Omega]", "*", "t"}], "-", RowBox[{"k", "*", "x"}], "+", "0"}], "]"}]}], "\[IndentingNewLine]", RowBox[{"\[Omega]", "=", RowBox[{"2", "*", "\[Pi]"}]}], "\[IndentingNewLine]", RowBox[{"k", "=", RowBox[{"2", "*", "\[Pi]"}]}], "\[IndentingNewLine]", RowBox[{"Z", "=", "1"}]}], "Input", CellChangeTimes->{{3.47321987524168*^9, 3.473220073947208*^9}, { 3.473220195289543*^9, 3.473220202028597*^9}, {3.4732202455848722`*^9, 3.47322024588756*^9}, {3.473220296299506*^9, 3.473220322612138*^9}, { 3.473363739219914*^9, 3.4733637499106007`*^9}, 3.473442161699765*^9, { 3.473468980722478*^9, 3.47346898958486*^9}, {3.4734691928703938`*^9, 3.473469247284136*^9}, {3.4734762100360928`*^9, 3.473476210820591*^9}, { 3.47464369692527*^9, 3.474643731468542*^9}, {3.4746440417449703`*^9, 3.474644045328919*^9}, 3.474644298127861*^9, {3.4746450395338182`*^9, 3.474645040287876*^9}, {3.4746456683660393`*^9, 3.4746456691479187`*^9}, { 3.4746825649753113`*^9, 3.474682588878072*^9}, {3.4746826436025887`*^9, 3.474682672653356*^9}, {3.506086044381668*^9, 3.506086068996378*^9}, { 3.506086368452426*^9, 3.50608637277752*^9}, {3.5060864645015087`*^9, 3.506086469514893*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"KEtr", "[", RowBox[{"x_", ",", "t_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Z", "/", "2"}], "/", RowBox[{"(", RowBox[{"\[Omega]", "/", "k"}], ")"}]}], "*", RowBox[{ RowBox[{"(", RowBox[{"D", "[", RowBox[{ RowBox[{"\[Phi]", "[", RowBox[{"x", ",", "w"}], "]"}], ",", "w"}], "]"}], ")"}], "^", "2"}]}], "/.", RowBox[{"w", "\[Rule]", "t"}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"PEtr", "[", RowBox[{"x_", ",", "t_"}], "]"}], ":=", RowBox[{ RowBox[{"Z", "*", RowBox[{ RowBox[{"(", RowBox[{"\[Omega]", "/", "k"}], ")"}], "/", "2"}], "*", RowBox[{ RowBox[{"(", RowBox[{"D", "[", RowBox[{ RowBox[{"\[Phi]", "[", RowBox[{"w", ",", "t"}], "]"}], ",", "w"}], "]"}], ")"}], "^", "2"}]}], "/.", RowBox[{"w", "\[Rule]", "x"}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Wtr", "[", RowBox[{"x_", ",", "t_"}], "]"}], ":=", RowBox[{ RowBox[{"KE", "[", RowBox[{"x", ",", "t"}], "]"}], "+", RowBox[{"PE", "[", RowBox[{"x", ",", "t"}], "]"}]}]}]}], "Input", CellChangeTimes->{{3.4734762214357157`*^9, 3.4734762219786882`*^9}, { 3.474643782979924*^9, 3.47464389488978*^9}, {3.474643948019971*^9, 3.474643985984314*^9}, {3.474644083468215*^9, 3.4746440993284807`*^9}, 3.474644715874096*^9, {3.474644955011422*^9, 3.474644956177236*^9}, { 3.474645257941094*^9, 3.4746453199619293`*^9}, 3.474645390050811*^9, { 3.4746831390638742`*^9, 3.474683159192067*^9}, 3.4746841482664413`*^9, 3.474684628974791*^9, {3.4746846635818663`*^9, 3.474684695858436*^9}, { 3.47468473989067*^9, 3.474684746658929*^9}, 3.474684777894044*^9, { 3.4746849113555202`*^9, 3.474684925265443*^9}, 3.474685061916651*^9, { 3.551556514821599*^9, 3.551556518097986*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"KEtr", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{"t", "\[Rule]", "0"}], "}"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"PEtr", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{"t", "\[Rule]", "0"}], "}"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Wtr", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{"t", "\[Rule]", "0"}], "}"}]}]}], "Input", CellChangeTimes->{{3.474645185943926*^9, 3.474645212577402*^9}, { 3.474645475481677*^9, 3.474645526201631*^9}, {3.474645720212001*^9, 3.4746457374441833`*^9}, {3.4746827007482*^9, 3.4746827317415657`*^9}, { 3.47468277235089*^9, 3.474682775871688*^9}, {3.474683086398398*^9, 3.474683090720456*^9}, {3.4746841940693827`*^9, 3.474684195129929*^9}, 3.506085915216004*^9, {3.5060861560381823`*^9, 3.506086158468569*^9}, { 3.5060864753593817`*^9, 3.506086478750358*^9}, {3.551556519295723*^9, 3.551556522160616*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"KEtr", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"t", "\[Rule]", "0"}]}], "}"}]}], ",", RowBox[{ RowBox[{"PEtr", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"t", "\[Rule]", "0"}]}], "}"}]}], ",", " ", RowBox[{ RowBox[{"Wtr", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"t", "\[Rule]", "0"}]}], "}"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "\"\<\!\(\* StyleBox[\"KE\", FontColor->RGBColor[1, 0, 0]]\),\!\(\* StyleBox[\"PE\", FontColor->RGBColor[0, 0, 1]]\),\!\(\* StyleBox[\"W\", FontColor->GrayLevel[0]]\)\>\""}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "Automatic"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Red", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Blue", ",", " ", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}]}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.474645621059373*^9, 3.474645633492831*^9}, { 3.474645749904531*^9, 3.4746457792511997`*^9}, 3.474645907155162*^9, { 3.474645949865087*^9, 3.474645978992264*^9}, {3.5060857274807034`*^9, 3.5060857278807707`*^9}, {3.5060863321351957`*^9, 3.506086349497436*^9}, { 3.537476126682723*^9, 3.537476151052205*^9}, {3.551556525157083*^9, 3.551556530619598*^9}}], Cell[BoxData[ RowBox[{"Animate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"KEtr", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}]}], "}"}]}], ",", RowBox[{ RowBox[{"PEtr", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}]}], "}"}]}], ",", " ", RowBox[{ RowBox[{"Wtr", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}]}], "}"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "\"\<\!\(\* StyleBox[\"KE\", FontColor->RGBColor[1, 0, 0]]\),\!\(\* StyleBox[\"PE\", FontColor->RGBColor[0, 0, 1]]\),\!\(\* StyleBox[\"W\", FontColor->GrayLevel[0]]\)\>\""}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "Automatic"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Red", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Blue", ",", " ", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}]}], "}"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", RowBox[{"2", "*", "\[Pi]"}]}], "}"}], ",", " ", RowBox[{"AnimationRate", "\[Rule]", ".05"}]}], "]"}]], "Input", CellChangeTimes->{{3.473468681858625*^9, 3.4734687099451036`*^9}, { 3.47346876528165*^9, 3.473468766613312*^9}, {3.473468855066791*^9, 3.473468861529861*^9}, {3.47346952785251*^9, 3.473469560862692*^9}, { 3.4734696825338097`*^9, 3.473469791022485*^9}, {3.473469935779962*^9, 3.473469961012698*^9}, 3.4734699966778812`*^9, 3.4734700470359697`*^9, { 3.4734701845834208`*^9, 3.473470187950139*^9}, {3.473470231502966*^9, 3.4734702657715693`*^9}, {3.4734704291666718`*^9, 3.4734704330748043`*^9}, {3.4734704735718327`*^9, 3.473470480906793*^9}, 3.473470607931302*^9, {3.47347069842999*^9, 3.4734707475622177`*^9}, { 3.4734720327350616`*^9, 3.4734720537449093`*^9}, {3.473472119558918*^9, 3.473472157647152*^9}, {3.473472243280195*^9, 3.473472340909021*^9}, { 3.474643995434366*^9, 3.474644049824279*^9}, {3.474644119487669*^9, 3.4746442364339647`*^9}, {3.474644324280504*^9, 3.474644355349601*^9}, { 3.474644428198427*^9, 3.4746444549615173`*^9}, 3.474644684601719*^9, { 3.474644774603016*^9, 3.47464480579154*^9}, 3.474645577128414*^9, 3.474646011572177*^9, {3.506085681525713*^9, 3.506085719416144*^9}, { 3.506086396625372*^9, 3.506086414109003*^9}, {3.537476028558361*^9, 3.537476116615769*^9}, {3.53747617984181*^9, 3.5374762785331078`*^9}, 3.537476529224267*^9, {3.55155653480552*^9, 3.551556539349489*^9}}], Cell[TextData[StyleBox["Standing wave", "Subtitle"]], "Text", CellChangeTimes->{{3.473472482411351*^9, 3.4734725034239473`*^9}, { 3.473472569742597*^9, 3.4734725709423923`*^9}, {3.474643702935645*^9, 3.474643705501945*^9}, {3.537476333361525*^9, 3.5374763339129744`*^9}, { 3.551555264277761*^9, 3.551555268369376*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"\[CapitalPhi]", "[", RowBox[{"x_", ",", "t_"}], "]"}], ":=", RowBox[{ RowBox[{"Sin", "[", RowBox[{"\[Omega]", "*", "t"}], "]"}], "*", RowBox[{"Sin", "[", RowBox[{"k", "*", "x"}], "]"}]}]}], "\[IndentingNewLine]", RowBox[{"\[Omega]", "=", RowBox[{"2", "*", "\[Pi]"}]}], "\[IndentingNewLine]", RowBox[{"k", "=", RowBox[{"2", "*", "\[Pi]"}]}], "\[IndentingNewLine]", RowBox[{"Z", "=", "1"}]}], "Input", CellChangeTimes->{{3.47321987524168*^9, 3.473220073947208*^9}, { 3.473220195289543*^9, 3.473220202028597*^9}, {3.4732202455848722`*^9, 3.47322024588756*^9}, {3.473220296299506*^9, 3.473220322612138*^9}, { 3.473363739219914*^9, 3.4733637499106007`*^9}, 3.473442161699765*^9, { 3.473468980722478*^9, 3.47346898958486*^9}, {3.4734691928703938`*^9, 3.473469247284136*^9}, {3.4734762100360928`*^9, 3.473476210820591*^9}, { 3.47464369692527*^9, 3.474643731468542*^9}, {3.4746440417449703`*^9, 3.474644045328919*^9}, 3.474644298127861*^9, {3.4746450395338182`*^9, 3.474645040287876*^9}, {3.4746456683660393`*^9, 3.4746456691479187`*^9}, { 3.4746825649753113`*^9, 3.474682588878072*^9}, {3.4746826436025887`*^9, 3.474682672653356*^9}, {3.506086044381668*^9, 3.506086068996378*^9}, { 3.506086368452426*^9, 3.50608637277752*^9}, {3.5060864645015087`*^9, 3.506086469514893*^9}, {3.551555288742041*^9, 3.551555314192333*^9}, { 3.5515554808866453`*^9, 3.5515555102423477`*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"KEst", "[", RowBox[{"x_", ",", "t_"}], "]"}], ":=", RowBox[{ RowBox[{ RowBox[{ RowBox[{"Z", "/", "2"}], "/", RowBox[{"(", RowBox[{"\[Omega]", "/", "k"}], ")"}]}], "*", RowBox[{ RowBox[{"(", RowBox[{"D", "[", RowBox[{ RowBox[{"\[CapitalPhi]", "[", RowBox[{"x", ",", "w"}], "]"}], ",", "w"}], "]"}], ")"}], "^", "2"}]}], "/.", RowBox[{"w", "\[Rule]", "t"}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"PEst", "[", RowBox[{"x_", ",", "t_"}], "]"}], ":=", RowBox[{ RowBox[{"Z", "*", RowBox[{ RowBox[{"(", RowBox[{"\[Omega]", "/", "k"}], ")"}], "/", "2"}], "*", RowBox[{ RowBox[{"(", RowBox[{"D", "[", RowBox[{ RowBox[{"\[CapitalPhi]", "[", RowBox[{"w", ",", "t"}], "]"}], ",", "w"}], "]"}], ")"}], "^", "2"}]}], "/.", RowBox[{"w", "\[Rule]", "x"}]}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Wst", "[", RowBox[{"x_", ",", "t_"}], "]"}], ":=", RowBox[{ RowBox[{"KE", "[", RowBox[{"x", ",", "t"}], "]"}], "+", RowBox[{"PE", "[", RowBox[{"x", ",", "t"}], "]"}]}]}]}], "Input", CellChangeTimes->{{3.4734762214357157`*^9, 3.4734762219786882`*^9}, { 3.474643782979924*^9, 3.47464389488978*^9}, {3.474643948019971*^9, 3.474643985984314*^9}, {3.474644083468215*^9, 3.4746440993284807`*^9}, 3.474644715874096*^9, {3.474644955011422*^9, 3.474644956177236*^9}, { 3.474645257941094*^9, 3.4746453199619293`*^9}, 3.474645390050811*^9, { 3.4746831390638742`*^9, 3.474683159192067*^9}, 3.4746841482664413`*^9, 3.474684628974791*^9, {3.4746846635818663`*^9, 3.474684695858436*^9}, { 3.47468473989067*^9, 3.474684746658929*^9}, 3.474684777894044*^9, { 3.4746849113555202`*^9, 3.474684925265443*^9}, 3.474685061916651*^9, { 3.551555370524012*^9, 3.551555414936902*^9}}], Cell[BoxData[{ RowBox[{ RowBox[{"KEst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{"t", "\[Rule]", "0"}], "}"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"PEst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{"t", "\[Rule]", "0"}], "}"}]}], "\[IndentingNewLine]", RowBox[{ RowBox[{"Wst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{"t", "\[Rule]", "0"}], "}"}]}]}], "Input", CellChangeTimes->{{3.474645185943926*^9, 3.474645212577402*^9}, { 3.474645475481677*^9, 3.474645526201631*^9}, {3.474645720212001*^9, 3.4746457374441833`*^9}, {3.4746827007482*^9, 3.4746827317415657`*^9}, { 3.47468277235089*^9, 3.474682775871688*^9}, {3.474683086398398*^9, 3.474683090720456*^9}, {3.4746841940693827`*^9, 3.474684195129929*^9}, 3.506085915216004*^9, {3.5060861560381823`*^9, 3.506086158468569*^9}, { 3.5060864753593817`*^9, 3.506086478750358*^9}, {3.5515554201800833`*^9, 3.551555426409202*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{"KEst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{"t", "\[Rule]", "0"}], "}"}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "\"\<\!\(\* StyleBox[\"KE\", FontColor->RGBColor[1, 0, 0]]\)\>\""}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", RowBox[{"{", RowBox[{"0", ",", "40"}], "}"}]}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{"Red", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.474682767911477*^9, 3.474682817457797*^9}, { 3.474682917571705*^9, 3.4746829195320587`*^9}, {3.474683007694663*^9, 3.4746830532340193`*^9}, {3.474683097581279*^9, 3.474683097953128*^9}, { 3.4746831502665253`*^9, 3.474683150868453*^9}, {3.474683478205449*^9, 3.4746834788570423`*^9}, {3.474683632910795*^9, 3.474683633988922*^9}, { 3.474683693276936*^9, 3.474683738215349*^9}, {3.474684216707549*^9, 3.474684226321472*^9}, 3.506085950807592*^9, {3.50608621252283*^9, 3.506086224993231*^9}, 3.537476360736977*^9, {3.5374763965194483`*^9, 3.537476457447607*^9}, {3.5515554312023897`*^9, 3.551555431371748*^9}}], Cell[BoxData[ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"KEst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"t", "\[Rule]", "0"}]}], "}"}]}], ",", RowBox[{ RowBox[{"PEst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"t", "\[Rule]", "0"}]}], "}"}]}], ",", " ", RowBox[{ RowBox[{"Wst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"t", "\[Rule]", "0"}]}], "}"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "\"\<\!\(\* StyleBox[\"KE\", FontColor->RGBColor[1, 0, 0]]\),\!\(\* StyleBox[\"PE\", FontColor->RGBColor[0, 0, 1]]\),\!\(\* StyleBox[\"W\", FontColor->GrayLevel[0]]\)\>\""}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "Automatic"}], ",", " ", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Red", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Blue", ",", " ", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}]}], "}"}]}]}], "]"}]], "Input", CellChangeTimes->{{3.474645621059373*^9, 3.474645633492831*^9}, { 3.474645749904531*^9, 3.4746457792511997`*^9}, 3.474645907155162*^9, { 3.474645949865087*^9, 3.474645978992264*^9}, {3.5060857274807034`*^9, 3.5060857278807707`*^9}, {3.5060863321351957`*^9, 3.506086349497436*^9}, { 3.537476126682723*^9, 3.537476151052205*^9}, {3.551555435211606*^9, 3.551555442371736*^9}, {3.551555527014271*^9, 3.55155552712392*^9}}], Cell[BoxData[ RowBox[{"Animate", "[", RowBox[{ RowBox[{"Plot", "[", RowBox[{ RowBox[{"{", RowBox[{ RowBox[{ RowBox[{"KEst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}]}], "}"}]}], ",", RowBox[{ RowBox[{"PEst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}]}], "}"}]}], ",", " ", RowBox[{ RowBox[{"Wst", "[", RowBox[{"x", ",", "t"}], "]"}], "/.", RowBox[{"{", RowBox[{ RowBox[{"Z", "\[Rule]", "1"}], ",", RowBox[{"\[Omega]", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}], ",", RowBox[{"k", "\[Rule]", RowBox[{"2", "*", "\[Pi]"}]}]}], "}"}]}]}], "}"}], ",", RowBox[{"{", RowBox[{"x", ",", "0", ",", "5"}], "}"}], ",", RowBox[{"AxesLabel", "\[Rule]", RowBox[{"{", RowBox[{"x", ",", "\"\<\!\(\* StyleBox[\"KE\", FontColor->RGBColor[1, 0, 0]]\),\!\(\* StyleBox[\"PE\", FontColor->RGBColor[0, 0, 1]]\),\!\(\* StyleBox[\"W\", FontColor->GrayLevel[0]]\)\>\""}], "}"}]}], ",", RowBox[{"PlotRange", "\[Rule]", "Automatic"}], ",", RowBox[{"PlotStyle", "\[Rule]", RowBox[{"{", RowBox[{ RowBox[{"{", RowBox[{"Red", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Blue", ",", " ", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}], ",", RowBox[{"{", RowBox[{"Black", ",", RowBox[{"AbsoluteThickness", "[", "2", "]"}]}], "}"}]}], "}"}]}]}], "]"}], ",", RowBox[{"{", RowBox[{"t", ",", "0", ",", RowBox[{"2", "*", "\[Pi]"}]}], "}"}], ",", " ", RowBox[{"AnimationRate", "\[Rule]", ".05"}]}], "]"}]], "Input", CellChangeTimes->{{3.473468681858625*^9, 3.4734687099451036`*^9}, { 3.47346876528165*^9, 3.473468766613312*^9}, {3.473468855066791*^9, 3.473468861529861*^9}, {3.47346952785251*^9, 3.473469560862692*^9}, { 3.4734696825338097`*^9, 3.473469791022485*^9}, {3.473469935779962*^9, 3.473469961012698*^9}, 3.4734699966778812`*^9, 3.4734700470359697`*^9, { 3.4734701845834208`*^9, 3.473470187950139*^9}, {3.473470231502966*^9, 3.4734702657715693`*^9}, {3.4734704291666718`*^9, 3.4734704330748043`*^9}, {3.4734704735718327`*^9, 3.473470480906793*^9}, 3.473470607931302*^9, {3.47347069842999*^9, 3.4734707475622177`*^9}, { 3.4734720327350616`*^9, 3.4734720537449093`*^9}, {3.473472119558918*^9, 3.473472157647152*^9}, {3.473472243280195*^9, 3.473472340909021*^9}, { 3.474643995434366*^9, 3.474644049824279*^9}, {3.474644119487669*^9, 3.4746442364339647`*^9}, {3.474644324280504*^9, 3.474644355349601*^9}, { 3.474644428198427*^9, 3.4746444549615173`*^9}, 3.474644684601719*^9, { 3.474644774603016*^9, 3.47464480579154*^9}, 3.474645577128414*^9, 3.474646011572177*^9, {3.506085681525713*^9, 3.506085719416144*^9}, { 3.506086396625372*^9, 3.506086414109003*^9}, {3.537476028558361*^9, 3.537476116615769*^9}, {3.53747617984181*^9, 3.5374762785331078`*^9}, 3.537476529224267*^9, {3.551555450230791*^9, 3.551555457443007*^9}}] }, WindowSize->{1276, 756}, WindowMargins->{{0, Automatic}, {Automatic, 0}}, FrontEndVersion->"7.0 for Mac OS X x86 (32-bit) (February 18, 2009)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[545, 20, 1015, 18, 125, "Text"], Cell[1563, 40, 278, 3, 38, "Text"], Cell[1844, 45, 1354, 25, 73, "Input"], Cell[3201, 72, 1899, 51, 58, "Input"], Cell[5103, 125, 1014, 23, 58, "Input"], Cell[6120, 150, 2503, 68, 43, "Input"], Cell[8626, 220, 3655, 84, 58, "Input"], Cell[12284, 306, 326, 4, 38, "Text"], Cell[12613, 312, 1482, 27, 73, "Input"], Cell[14098, 341, 1913, 51, 58, "Input"], Cell[16014, 394, 1016, 23, 58, "Input"], Cell[17033, 419, 1386, 32, 27, "Input"], Cell[18422, 453, 2548, 68, 43, "Input"], Cell[20973, 523, 3656, 84, 58, "Input"] } ] *) (* End of internal cache information *)