(* 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[     32237,        647]
NotebookOptionsPosition[     15630,        344]
NotebookOutlinePosition[     32035,        638]
CellTagsIndexPosition[     31992,        635]
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{

Cell[CellGroupData[{
Cell[TextData[{
 "Damped pendulum swinging in a fluid\n",
 StyleBox["by Olaf Ellers, Ph.D., Research Associate, Biology and Math \
Departments, Bowdoin College", "Text",
  FontFamily->"Arial",
  FontSize->14],
 " \n",
 StyleBox["This model is of a pendulum swinging in a fluid in earth's gravity \
and is based on Neill et al., 2007.  See below for things to try, assumptions \
and range of variables.\n",
  FontSize->14]
}], "Title",
 Evaluatable->False,
 CellChangeTimes->{{3.449845031651*^9, 3.449845036105*^9}, {
   3.4500062297759447`*^9, 3.4500062341149445`*^9}, 3.450015257863945*^9, {
   3.450016247826945*^9, 3.450016329838945*^9}, {3.450183332638337*^9, 
   3.4501833638683367`*^9}, {3.450183609898337*^9, 3.4501836254133368`*^9}}],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Manipulate", "[", 
  RowBox[{
   RowBox[{"If", "[", 
    RowBox[{
     RowBox[{"\[Rho]o", ">", "\[Rho]f"}], ",", 
     RowBox[{"Plot", "[", 
      RowBox[{
       RowBox[{"l", " ", 
        FractionBox[
         RowBox[{"2", " ", "\[Pi]"}], "360"], "\[Alpha]", " ", 
        SuperscriptBox["\[ExponentialE]", 
         RowBox[{
          RowBox[{"-", "t"}], " ", "\[Lambda]"}]], " ", 
        RowBox[{"Cos", "[", 
         RowBox[{
          RowBox[{
           FractionBox[
            RowBox[{"2", " ", "\[Pi]"}], "360"], "\[Delta]"}], "-", " ", 
          RowBox[{"t", " ", 
           SqrtBox[
            RowBox[{
             RowBox[{"-", 
              SuperscriptBox["\[Lambda]", "2"]}], "+", 
             FractionBox[
              RowBox[{"9.8", " ", 
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"-", "\[Rho]f"}], "+", "\[Rho]o"}], ")"}]}], 
              RowBox[{"l", " ", 
               RowBox[{"(", 
                RowBox[{
                 RowBox[{"\[Kappa]", " ", "\[Rho]f"}], "+", "\[Rho]o"}], 
                ")"}]}]]}]]}]}], "]"}]}], " ", ",", 
       RowBox[{"{", 
        RowBox[{"t", ",", "0", ",", "100"}], "}"}], ",", 
       RowBox[{"PlotStyle", "\[Rule]", "Red"}], ",", 
       RowBox[{"PlotRange", "\[Rule]", "All"}], ",", 
       RowBox[{"AxesOrigin", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"0", ",", "0"}], "}"}]}], ",", 
       RowBox[{"Frame", "\[Rule]", "True"}], ",", 
       RowBox[{"FrameLabel", "\[Rule]", 
        RowBox[{"{", 
         RowBox[{"\"\<time (s)\>\"", ",", "\"\<displacement (meters)\>\""}], 
         "}"}]}], ",", 
       RowBox[{"LabelStyle", "\[Rule]", "Large"}]}], "]"}], ",", 
     RowBox[{
     "Print", "[", 
      "\"\<Error, Object density must be greater than fluid density\>\"", 
      "]"}]}], "]"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "\[Alpha]", ",", "2", ",", 
       "\"\<initial angular amplitude (Degree), \[Alpha]\>\""}], "}"}], ",", 
     "0.1", ",", "10", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   "\[IndentingNewLine]", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "\[Delta]", ",", "0", ",", "\"\<phase shift (Degree), \[Delta]\>\""}], 
      "}"}], ",", 
     RowBox[{"-", "180"}], ",", "180", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "\[Lambda]", ",", "0.01", ",", 
       "\"\<damping constant (\!\(\*SuperscriptBox[\(s\), \(-1\)]\)), \
\[Lambda]\>\""}], "}"}], ",", "0.001", ",", "1", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{"l", ",", "3", ",", "\"\<string length (m), l\>\""}], "}"}], 
     ",", "0.01", ",", "3", "\[IndentingNewLine]", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "\[Rho]o", ",", "7860", ",", 
       "\"\<bob density (kg \!\(\*SuperscriptBox[\(m\), \(-3\)]\)), \[Rho]o\>\
\""}], "}"}], ",", "998", ",", "8480", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "\[Rho]f", ",", "998", ",", 
       "\"\<fluid density (kg \!\(\*SuperscriptBox[\(m\), \(-3\)]\)), \[Rho]f\
\>\""}], "}"}], ",", "1.205", ",", "2870", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"{", 
    RowBox[{
     RowBox[{"{", 
      RowBox[{
      "\[Kappa]", ",", "0.5", ",", 
       "\"\<coefficient of added mass, \[Kappa]\>\""}], "}"}], ",", "0.3", 
     ",", "3", ",", 
     RowBox[{"Appearance", "\[Rule]", "\"\<Labeled\>\""}]}], "}"}], ",", 
   RowBox[{"LabelStyle", "->", "Large"}]}], "]"}]], "Input",
 CellChangeTimes->{{3.446483938816*^9, 3.446483939127*^9}, 3.446484013032*^9, 
   3.446484048921*^9, {3.4464841916809998`*^9, 3.4464841990220003`*^9}, {
   3.450016649177945*^9, 3.450016649646945*^9}, {3.450016917620945*^9, 
   3.4500169181969447`*^9}, {3.450016982059945*^9, 3.4500169888109446`*^9}, {
   3.450021963590001*^9, 3.450021996749946*^9}, {3.4500220839971123`*^9, 
   3.450022111785446*^9}, {3.450023144117053*^9, 3.4500231443281164`*^9}, {
   3.450026995166*^9, 3.450026996817*^9}, {3.450027222145*^9, 
   3.4500272236879997`*^9}, {3.450027367443*^9, 3.4500273681470003`*^9}, {
   3.450027414051*^9, 3.450027416822*^9}, {3.4500276128570004`*^9, 
   3.4500276301029997`*^9}, 3.450027939519*^9, 3.450035150102*^9, 
   3.4501754480283365`*^9, {3.450175630457337*^9, 3.450175632935337*^9}, {
   3.450176452796337*^9, 3.4501765436903367`*^9}, 3.4501765775093365`*^9, {
   3.450177178812337*^9, 3.450177182340337*^9}, {3.450177219814337*^9, 
   3.450177266893337*^9}, {3.450177298221337*^9, 3.450177299188337*^9}, {
   3.450177337494337*^9, 3.450177370181337*^9}, 3.450177492185337*^9, {
   3.4501775803253365`*^9, 3.450177580564337*^9}, 3.450180280350337*^9, {
   3.450180386847337*^9, 3.4501805538163366`*^9}, 3.450182250402337*^9, {
   3.4501823539833364`*^9, 3.450182405386337*^9}, {3.4501824585023365`*^9, 
   3.450182459074337*^9}}],

Cell[BoxData[
 TagBox[
  StyleBox[
   DynamicModuleBox[{$CellContext`l$$ = 3, $CellContext`\[Alpha]$$ = 
    2, $CellContext`\[Delta]$$ = 0, $CellContext`\[Kappa]$$ = 
    0.7, $CellContext`\[Lambda]$$ = 0.01, $CellContext`\[Rho]f$$ = 
    998, $CellContext`\[Rho]o$$ = 7860, Typeset`show$$ = True, 
    Typeset`bookmarkList$$ = {}, Typeset`bookmarkMode$$ = "Menu", 
    Typeset`animator$$, Typeset`animvar$$ = 1, Typeset`name$$ = 
    "\"untitled\"", Typeset`specs$$ = {{{
       Hold[$CellContext`\[Alpha]$$], 2, 
       "initial angular amplitude (Degree), \[Alpha]"}, 0.1, 10}, {{
       Hold[$CellContext`\[Delta]$$], 0, 
       "phase shift (Degree), \[Delta]"}, -180, 180}, {{
       Hold[$CellContext`\[Lambda]$$], 0.01, 
       "damping constant (\!\(\*SuperscriptBox[\(s\), \(-1\)]\)), \[Lambda]"},
       0.001, 1}, {{
       Hold[$CellContext`l$$], 3, "string length (m), l"}, 0.01, 3}, {{
       Hold[$CellContext`\[Rho]o$$], 7860, 
       "bob density (kg \!\(\*SuperscriptBox[\(m\), \(-3\)]\)), \[Rho]o"}, 
      998, 8480}, {{
       Hold[$CellContext`\[Rho]f$$], 998, 
       "fluid density (kg \!\(\*SuperscriptBox[\(m\), \(-3\)]\)), \[Rho]f"}, 
      1.205, 2870}, {{
       Hold[$CellContext`\[Kappa]$$], 0.7, 
       "coefficient of added mass, \[Kappa]"}, 0.3, 3}}, Typeset`size$$ = {
    360., {122., 126.}}, Typeset`update$$ = 0, Typeset`initDone$$, 
    Typeset`skipInitDone$$ = True, $CellContext`\[Alpha]$85687$$ = 
    0, $CellContext`\[Delta]$85688$$ = 0, $CellContext`\[Lambda]$85689$$ = 
    0, $CellContext`l$85690$$ = 0, $CellContext`\[Rho]o$85691$$ = 
    0, $CellContext`\[Rho]f$85692$$ = 0, $CellContext`\[Kappa]$85693$$ = 0}, 
    DynamicBox[Manipulate`ManipulateBoxes[
     1, StandardForm, 
      "Variables" :> {$CellContext`l$$ = 3, $CellContext`\[Alpha]$$ = 
        2, $CellContext`\[Delta]$$ = 0, $CellContext`\[Kappa]$$ = 
        0.7, $CellContext`\[Lambda]$$ = 0.01, $CellContext`\[Rho]f$$ = 
        998, $CellContext`\[Rho]o$$ = 7860}, "ControllerVariables" :> {
        Hold[$CellContext`\[Alpha]$$, $CellContext`\[Alpha]$85687$$, 0], 
        Hold[$CellContext`\[Delta]$$, $CellContext`\[Delta]$85688$$, 0], 
        Hold[$CellContext`\[Lambda]$$, $CellContext`\[Lambda]$85689$$, 0], 
        Hold[$CellContext`l$$, $CellContext`l$85690$$, 0], 
        Hold[$CellContext`\[Rho]o$$, $CellContext`\[Rho]o$85691$$, 0], 
        Hold[$CellContext`\[Rho]f$$, $CellContext`\[Rho]f$85692$$, 0], 
        Hold[$CellContext`\[Kappa]$$, $CellContext`\[Kappa]$85693$$, 0]}, 
      "OtherVariables" :> {
       Typeset`show$$, Typeset`bookmarkList$$, Typeset`bookmarkMode$$, 
        Typeset`animator$$, Typeset`animvar$$, Typeset`name$$, 
        Typeset`specs$$, Typeset`size$$, Typeset`update$$, Typeset`initDone$$,
         Typeset`skipInitDone$$}, "Body" :> 
      If[$CellContext`\[Rho]o$$ > $CellContext`\[Rho]f$$, 
        Plot[((($CellContext`l$$ (2 (Pi/360))) $CellContext`\[Alpha]$$) 
          E^((-$CellContext`t) $CellContext`\[Lambda]$$)) 
         Cos[(2 (Pi/
              360)) $CellContext`\[Delta]$$ - $CellContext`t (-$CellContext`\
\[Lambda]$$^2 + 
             9.8 ((-$CellContext`\[Rho]f$$ + \
$CellContext`\[Rho]o$$)/($CellContext`l$$ ($CellContext`\[Kappa]$$ \
$CellContext`\[Rho]f$$ + $CellContext`\[Rho]o$$))))^
            Rational[1, 2]], {$CellContext`t, 0, 100}, PlotStyle -> Red, 
         PlotRange -> All, AxesOrigin -> {0, 0}, Frame -> True, 
         FrameLabel -> {"time (s)", "displacement (meters)"}, LabelStyle -> 
         Large], 
        Print["Error, Object density must be greater than fluid density"]], 
      "Specifications" :> {{{$CellContext`\[Alpha]$$, 2, 
          "initial angular amplitude (Degree), \[Alpha]"}, 0.1, 10, 
         Appearance -> 
         "Labeled"}, {{$CellContext`\[Delta]$$, 0, 
          "phase shift (Degree), \[Delta]"}, -180, 180, Appearance -> 
         "Labeled"}, {{$CellContext`\[Lambda]$$, 0.01, 
          "damping constant (\!\(\*SuperscriptBox[\(s\), \(-1\)]\)), \
\[Lambda]"}, 0.001, 1, Appearance -> 
         "Labeled"}, {{$CellContext`l$$, 3, "string length (m), l"}, 0.01, 3, 
         Appearance -> 
         "Labeled"}, {{$CellContext`\[Rho]o$$, 7860, 
          "bob density (kg \!\(\*SuperscriptBox[\(m\), \(-3\)]\)), \[Rho]o"}, 
         998, 8480, Appearance -> 
         "Labeled"}, {{$CellContext`\[Rho]f$$, 998, 
          "fluid density (kg \!\(\*SuperscriptBox[\(m\), \(-3\)]\)), \
\[Rho]f"}, 1.205, 2870, Appearance -> 
         "Labeled"}, {{$CellContext`\[Kappa]$$, 0.7, 
          "coefficient of added mass, \[Kappa]"}, 0.3, 3, Appearance -> 
         "Labeled"}}, "Options" :> {LabelStyle -> Large}, 
      "DefaultOptions" :> {}],
     ImageSizeCache->{699., {297., 302.}},
     SingleEvaluation->True],
    Deinitialization:>None,
    DynamicModuleValues:>{},
    SynchronousInitialization->True,
    UnsavedVariables:>{Typeset`initDone$$},
    UntrackedVariables:>{Typeset`size$$}], "Manipulate",
   Deployed->True,
   StripOnInput->False],
  Manipulate`InterpretManipulate[1]]], "Output",
 CellChangeTimes->{
  3.4498450073389997`*^9, 3.450015348003945*^9, 3.4500156773959446`*^9, 
   3.450016651099945*^9, 3.4500169191379447`*^9, 3.4500219656976333`*^9, 
   3.4500219979523067`*^9, 3.450022112847765*^9, 3.4500231451263556`*^9, {
   3.450027928101*^9, 3.4500279419440002`*^9}, 3.4500288251610003`*^9, 
   3.450175449784337*^9, 3.450175642704337*^9, 3.450176620560337*^9, 
   3.450177183645337*^9, 3.4501772693483367`*^9, 3.4501773781933365`*^9, 
   3.450177496682337*^9, 3.4501805576533365`*^9, 3.450182253418337*^9, {
   3.450182393949337*^9, 3.450182406748337*^9}}]
}, {2}]],

Cell[TextData[{
 StyleBox["Things to try:\n(1) Try simulating experimental conditions in \
Neill et al. (2007).\n(2) Neill et al. (2007) found very low values of \
\[Lambda], but higher values of \[Lambda] may be realistic for smaller or \
less dense bobs, conditions that can be simulated here.\n(3) Neill et al. \
(2007) used bobs that were much denser than the fluid; try simulating bobs \
that are only slightly denser than the fluid.\n(4) Neill et al. (2007) used \
spherical bobs; try simulating the effects of bobs that are prolate spheroids \
by varying \[Kappa].",
  FontSize->14],
 StyleBox["\n\nAssumptions :\n(1) The small angle assumption is used, in \
which it is assumed that \[Theta] is approximately equal to Sin[\[Theta]].  \
For angles less than 10 degrees, the difference between \[Theta] and Sin[\
\[Theta]] is less than 5 %;\n(2) The bob is a point mass;\n(3) The string is \
weightless, has no resistance and does not bend or stretch.\n(4) Resistance \
from the fluid is modeled as a constant times velocity.\n",
  FontFamily->"Courier New",
  FontSize->14],
 "\n",
 StyleBox["Range of the variables:\n(1) The damping constant, \[Lambda], \
ranges from  0.001-1;\n(2) The bob density ranges from that of water at 20",
  FontSize->14],
 "\[Degree]",
 StyleBox["C to that of a brass bob;\n(3) The fluid density ranges from that \
of air at 20",
  FontSize->14],
 "\[Degree]",
 StyleBox["C to that of bromoform;\n(4) The range of the coefficient mass, ",
  FontSize->14],
 "\[Kappa]",
 StyleBox[", represents the range found experimentally for prolate spheroids \
of a width to length ratio ranging from 1:3 to 3:1 with ",
  FontSize->14],
 "\[Kappa]",
 StyleBox[" ranging approximately from 0.3-3; the initial value is set at \
0.5, which is the theoretically derived value for a sphere in water at 20",
  FontSize->14],
 "\[Degree]",
 StyleBox["C (see Daniel, 1985); note that Neill et al. (2007) obtained \
experimental values of ",
  FontSize->14],
 "\[Kappa] ",
 StyleBox["= 0.7 for steel and brass spheres in water.\n(5) Ensure that the \
bob density is higher than the fluid density, otherwise an error will occur.",
  FontSize->14]
}], "Input",
 PageWidth->WindowWidth,
 Evaluatable->False,
 CellChangeTimes->{{3.4500160280489445`*^9, 3.450016056293945*^9}, {
  3.4500161035559444`*^9, 3.4500161118369446`*^9}, {3.450016145912945*^9, 
  3.450016146970945*^9}, {3.450028549348*^9, 3.450028615264*^9}, {
  3.450183080947337*^9, 3.450183112879337*^9}, {3.450183208890337*^9, 
  3.450183210392337*^9}, {3.4501832903353367`*^9, 3.450183312273337*^9}},
 FontColor->GrayLevel[0]],

Cell[TextData[StyleBox["Citations :\n\tDaniel, T.L. (1985)  Cost of \
locomotion: unsteady medusan swimming.  J. Exp. Biol. 119 : 149 - 164.\n\t\
Neill, D., Livelybrooks, D., Donnelly, R.J. (2007)  A pendulum experimnet on \
added mass and the principle of equivalence.  Am. J. Phys. 75(3): 226 - 229.",
 FontFamily->"Arial",
 FontSize->11,
 FontWeight->"Plain"]], "Input",
 Evaluatable->False,
 CellChangeTimes->{{3.4500160280489445`*^9, 3.450016056293945*^9}, {
  3.4500161035559444`*^9, 3.4500161118369446`*^9}, {3.450016145912945*^9, 
  3.450016146970945*^9}, {3.450028549348*^9, 3.450028615264*^9}, {
  3.450175038404337*^9, 3.450175086593337*^9}, {3.4501751287003365`*^9, 
  3.450175135774337*^9}, {3.4501751704743366`*^9, 3.450175178155337*^9}},
 FontColor->GrayLevel[0]]
}, Open  ]]
},
WindowSize->{1264, 724},
WindowMargins->{{-8, Automatic}, {Automatic, -5}},
DockedCells->FEPrivate`If[
  FEPrivate`SameQ[FEPrivate`$ProductIDName, "MathematicaPlayer"], 
  FEPrivate`Join[{
    Cell[
     BoxData[
      GraphicsBox[
       RasterBox[CompressedData["
1:eJztXXlYU9e27/fe++Pe9757be9tax1AkUGQAMokiLMWB9Q60Dreaq2tA1Zb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        "], {{0, 0}, {516, 41}}, {0, 255}, ColorFunction -> RGBColor], 
       ImageSize -> {516, 41}, PlotRange -> {{0, 516}, {0, 41}}]], 
     "DockedCell", Background -> GrayLevel[0.866682], 
     CellFrame -> {{0, 0}, {0, 4}}, CellFrameColor -> 
     RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> {{0, 0}, {-3, 0}}, 
     CellFrameMargins -> 0, ContextMenu -> None, 
     ComponentwiseContextMenu -> {}], 
    Cell[
     BoxData[
      GridBox[{{
         GraphicsBox[
          RasterBox[CompressedData["
1:eJztWl1Ik1EYFrqNEoLMbHPmNkRrEhJERj93ra4cJvbDRIsyMk1pc03tTL1w
aD+LfkQIJBkR/dBFdtHFDLywCykqoqgLIYRu6jbb8me933e+HT/P2fZN+sZ0
vg9n43zfec973nPe57zvOWNFDS2OhnU5OTlG+LyBj1S/ikAgEAgEAoFAIBAI
xEpFMBh8jUgPYG0z7d7MAOYedm/Bko4Ca5tp92YGSCokle5AUiGpdAeSCkml
O0RS/R1tjEajUIHvyIhdehPyLNZjrVSAgT5CK1Tmf32e+/qcdYEy+/4+vKTd
oQJN89PjojbaHcrCzE8qn0RGfIxrEjcF0SomD49hYqDDUUSGKtUKWRMYz42L
pFJDg1RPamGdlRWGuuDi2Yl+WHkoiy72W6jjgFeSm/wWKEAScCvtCxWpSzxt
1FPU9dJ76Lt8UnEmcVMQrWImUQE6nKJB7sgUKpb4LcpEtHiFpEpEKim2TI8n
IhXv4pAHXCAJEAPIq7d5JFAOYYEGKHEstTbQAJKSx+XH5ZKKE+CmIFq1ZC/E
SBVXoboJyMliKZKKgyapwLlK1ohHKgpYYfGRbnNpg4c8dP3prtckFQ0gUm5K
miKpVZxnRZP4KcSziiU1bjhOobpJ2TtIqnhITipYZ7byydJfoDzMpT9ZWMo1
EHbgBBLyhOWzlmakUtKQnB/VuUYkFbWNjZXIJHEKnFVL0t+IXSQVU4iRKkUk
JxVzhJI7hirpDpXOGzJ5eFLFvMNORxAlaJZhmtmZStQGAvSQA/FECSksH/kt
VLMyokw5qHDOFU3ipiBaxZmtTSo8U2lBI1LF/BWNXZ0Y1LckLo9IqQdYIWdA
9T0uvPT2J2qjrUr2lGMRSzrq4eiIVIxFGC5bMZO4KYhWcWYnSn8gv3j7k+vJ
GbVaSNXt9fo6O/XVib9Tpa+sClLdvtB0q+WSvjqRVGucVA/q6p9V1+irE0m1
xkk1cuLk2O49+upEUq1xUg1X14yZraSrS0ed+H+q9GFV/J+qx25/u9U40Nqa
aUMQ2YMrFRWf8g0vDh9JvUvgYjPR+8KIyA5AyiNeb1Pe5ql840xxSV97eyq9
Hp1y3nE602waYoXC19GRqInIGHC57lY53Lm53/O2RQ3Fr6qqNXUG609/LLX1
ulOiHyL74D/XeLPxvPiexHDtsuulyexbv2GqwLRgNP8xl/W7XAQE1IUQ1nHw
zNl5o2XYoc09RLbC5/E8te26V9+gfskY5SPkuss1abLc2Ljpm9E8Z7FFt++c
POroJoQWn1wotQAPj9XMFZp/m6y9bndGpoNYCZBikbNuoqBwsPY4IxIrQJu+
trYf5pLRfOOXotJw6d7Zsv0LtkOPzzb1ENKjolagueVD5YGodUfEZH2372Cm
p4X4X/wDFcRtOg==
           "], {{0, 0}, {199, 30}}, {0, 255}, ColorFunction -> RGBColor], 
          ImageSize -> {199, 30}, PlotRange -> {{0, 199}, {0, 30}}], 
         ButtonBox[
          GraphicsBox[
           RasterBox[CompressedData["
1:eJztlDFuhFAMRJHS5w45Re6RI+wFcoOUtNtR0lJSUlNSUtNS0m9JXjTKaPQh
UfpgCeT1n2+Px15ebu9vt6eqqp55Xnm+/I/L/p+1bbtt277vvJumIcKbnwWs
73vBsHVdE1bXNQ55Ho8HMOEd3L9tWRZ+6tRBrrjEMAwigHO/37M6SII40zRB
Q7QLkpQWjKOu63RqGHHVIoOYYAR16oucinYGxUo2jqMIzPNMnpQRPF2nMkeS
cCBDXsm7ZNZp6oZRS3wsIBFNIYM2iY8gYmJA8imqawHcOAKqio4KSp4O7Qjp
K1nOUygasaG2hoKSaud3krkArggZzyhhTohP3Uz7E0mNu9g98oj26exOSTon
fRUtn8IUJL+W80gyuz6OW3mgrSXXEv5dSaRTaRz9KQpY/knxtVomKdFQxvFT
JZFR6pFBJWT5tbEvR9+H3F6S+GOSMC+DTHtrHYyh32Qu855cdhn2CUundjY=

            "], {{0, 0}, {55, 14}}, {0, 255}, ColorFunction -> RGBColor], 
           ImageSize -> {55, 14}, PlotRange -> {{0, 55}, {0, 14}}], 
          ButtonData -> {
            URL["http://store.wolfram.com/view/app/playerpro/"], None}, 
          ButtonNote -> "http://store.wolfram.com/view/app/playerpro/"], 
         GraphicsBox[
          
          RasterBox[{{{132, 132, 132}, {156, 155, 155}}, {{138, 137, 137}, {
           171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 
           137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 
           137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{
           138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 169, 
           169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {171, 
           169, 169}}, {{138, 137, 137}, {171, 169, 169}}, {{138, 137, 137}, {
           171, 169, 169}}, {{135, 135, 135}, {167, 166, 166}}}, {{0, 0}, {2, 
           14}}, {0, 255}, ColorFunction -> RGBColor], ImageSize -> {2, 14}, 
          PlotRange -> {{0, 2}, {0, 14}}], 
         ButtonBox[
          GraphicsBox[
           RasterBox[CompressedData["
1:eJztlSGSg2AMhTuzfu+wB1qzR+gF9gbIWhwSW4lEV1ZWYyvxSPZb3vAmDdDq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            "], {{0, 0}, {77, 14}}, {0, 255}, ColorFunction -> RGBColor], 
           ImageSize -> {77, 14}, PlotRange -> {{0, 77}, {0, 14}}], 
          ButtonData -> {
            URL[
            "http://www.wolfram.com/solutions/interactivedeployment/\
licensingterms.html"], None}, ButtonNote -> 
          "http://www.wolfram.com/solutions/interactivedeployment/\
licensingterms.html"]}}, ColumnsEqual -> False, 
       GridBoxAlignment -> {"Columns" -> {{Center}}, "Rows" -> {{Center}}}]], 
     "DockedCell", Background -> GrayLevel[0.494118], 
     CellFrame -> {{0, 0}, {4, 0}}, CellFrameColor -> 
     RGBColor[0.690074, 0.12871, 0.194598], CellMargins -> 0, 
     CellFrameMargins -> {{0, 0}, {0, -1}}, ContextMenu -> None, 
     ComponentwiseContextMenu -> {}, 
     ButtonBoxOptions -> {ButtonFunction :> (FrontEndExecute[{
          NotebookLocate[#2]}]& ), Appearance -> None, ButtonFrame -> None, 
       Evaluator -> None, Method -> "Queued"}]}, 
   FEPrivate`If[
    FEPrivate`SameQ[
     FrontEnd`CurrentValue[
      FrontEnd`EvaluationNotebook[], ScreenStyleEnvironment], "SlideShow"], {
    Inherited}, {}]], Inherited],
FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (November 10, 2008)",
StyleDefinitions->FrontEnd`FileName[{"Creative"}, "NaturalColor.nb", 
  CharacterEncoding -> "WindowsANSI"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{}
*)
(*CellTagsIndex
CellTagsIndex->{}
*)
(*NotebookFileOutline
Notebook[{
Cell[CellGroupData[{
Cell[567, 22, 741, 16, 181, "Title",
 Evaluatable->False],
Cell[CellGroupData[{
Cell[1333, 42, 5265, 125, 226, "Input"],
Cell[6601, 169, 5620, 101, 626, "Output"]
}, {2}]],
Cell[12233, 273, 2600, 53, 415, "Input",
 Evaluatable->False],
Cell[14836, 328, 778, 13, 69, "Input",
 Evaluatable->False]
}, Open  ]]
}
]
*)

(* End of internal cache information *)
(* NotebookSignature zxTrqTUDCl3WRAwxbbWzlWOB *)