(* Content-type: application/mathematica *) (*** Wolfram Notebook File ***) (* http://www.wolfram.com/nb *) (* CreatedBy='Mathematica 7.0' *) (*CacheID: 234*) (* Internal cache information: NotebookFileLineBreakTest NotebookFileLineBreakTest NotebookDataPosition[ 145, 7] NotebookDataLength[ 4339, 139] NotebookOptionsPosition[ 3717, 116] NotebookOutlinePosition[ 4062, 131] CellTagsIndexPosition[ 4019, 128] WindowFrame->Normal*) (* Beginning of Notebook Content *) Notebook[{ Cell[TextData[{ StyleBox["Pendulum\n\n", FontFamily->"Times New Roman", FontSize->28, FontWeight->"Bold"], StyleBox["Calculate the integral needed for the pendulum period.", FontFamily->"Times New Roman", FontSize->22] }], "Text", CellChangeTimes->{{3.5207833179296007`*^9, 3.520783355241384*^9}, 3.520783796186043*^9}], Cell[BoxData[ StyleBox[ RowBox[{"Clear", "[", RowBox[{"y", ",", "A"}], "]"}], FontFamily->"Courier New", FontSize->18]], "Input", CellChangeTimes->{{3.5207833583975735`*^9, 3.520783362897487*^9}, { 3.520786351402607*^9, 3.520786353105699*^9}, {3.520962650855196*^9, 3.5209626513239365`*^9}}], Cell[TextData[StyleBox["Enter the amplitude in degrees. The equals sign will \ display the result upon hitting shift and enter at the same time. A colon \ followed by an equals sign will suppress the output. ", FontFamily->"Times New Roman", FontSize->22]], "Text", CellChangeTimes->{{3.520783435349221*^9, 3.5207835019416924`*^9}, { 3.520962935959097*^9, 3.520962943396454*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"ampindegrees", "=", "90"}], FontFamily->"Courier New", FontSize->18]], "Input", CellChangeTimes->{{3.5207834557863283`*^9, 3.520783460442489*^9}, { 3.5207836205800395`*^9, 3.520783620689412*^9}, {3.520786251685771*^9, 3.520786271435392*^9}}], Cell["", "Text"], Cell[TextData[StyleBox["Convert to an amplitude in radians. Call it A ( we \ used theta max in class). There are two ways to write pi, either Esc-pi-Esc \ or Pi, remembering that the p is capitalized in the second expression.", FontFamily->"Times New Roman", FontSize->22]], "Text", CellChangeTimes->{{3.520783526113103*^9, 3.520783606549059*^9}, { 3.520783640501532*^9, 3.520783643829593*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"A", "=", RowBox[{"ampindegrees", "*", RowBox[{"Pi", "/", "180"}]}]}], FontFamily->"Courier New", FontSize->18]], "Input", CellChangeTimes->{{3.520783609908369*^9, 3.520783635032887*^9}, { 3.520786193905631*^9, 3.520786243264058*^9}}], Cell[TextData[StyleBox["This is the integral we want. In class we used \ \[Theta] instead of y. ", FontFamily->"Times New Roman", FontSize->22]], "Text", CellChangeTimes->{{3.520783688250615*^9, 3.520783726890498*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"Integrate", "[", RowBox[{ RowBox[{"1", "/", RowBox[{ RowBox[{"(", RowBox[{ RowBox[{"Cos", "[", "y", "]"}], "-", RowBox[{"Cos", "[", "A", "]"}]}], ")"}], "^", RowBox[{"(", RowBox[{"1", "/", "2"}], ")"}]}]}], ",", RowBox[{"{", RowBox[{"y", ",", "0", ",", "A"}], "}"}]}], "]"}], FontFamily->"Courier New", FontSize->18]], "Input", CellChangeTimes->{{3.520786052533345*^9, 3.520786099610566*^9}}], Cell[TextData[StyleBox["N[%] will give a numeric result to the previous \ expression.", FontFamily->"Times New Roman", FontSize->22]], "Text", CellChangeTimes->{{3.520786150062722*^9, 3.5207861701717114`*^9}}], Cell[BoxData[ StyleBox[ RowBox[{"N", "[", "%", "]"}], FontFamily->"Courier New", FontSize->18]], "Input", CellChangeTimes->{{3.5207861144852805`*^9, 3.520786117282102*^9}}] }, WindowSize->{616, 750}, WindowMargins->{{22, Automatic}, {Automatic, 69}}, FrontEndVersion->"7.0 for Microsoft Windows (32-bit) (February 18, 2009)", StyleDefinitions->"Default.nb" ] (* End of Notebook Content *) (* Internal cache information *) (*CellTagsOutline CellTagsIndex->{} *) (*CellTagsIndex CellTagsIndex->{} *) (*NotebookFileOutline Notebook[{ Cell[545, 20, 336, 10, 109, "Text"], Cell[884, 32, 308, 8, 36, "Input"], Cell[1195, 42, 386, 6, 123, "Text"], Cell[1584, 50, 287, 7, 36, "Input"], Cell[1874, 59, 16, 0, 29, "Text"], Cell[1893, 61, 401, 6, 123, "Text"], Cell[2297, 69, 285, 8, 36, "Input"], Cell[2585, 79, 223, 4, 67, "Text"], Cell[2811, 85, 504, 16, 64, "Input"], Cell[3318, 103, 212, 4, 67, "Text"], Cell[3533, 109, 180, 5, 36, "Input"] } ] *) (* End of internal cache information *)