(************** Content-type: application/mathematica ************** CreatedBy='Mathematica 5.2' Mathematica-Compatible Notebook This notebook can be used with any Mathematica-compatible application, such as Mathematica, MathReader or Publicon. The data for the notebook starts with the line containing stars above. To get the notebook into a Mathematica-compatible application, do one of the following: * Save the data starting with the line of stars above into a file with a name ending in .nb, then open the file inside the application; * Copy the data starting with the line of stars above to the clipboard, then use the Paste menu command inside the application. Data for notebooks contains only printable 7-bit ASCII and can be sent directly in email or through ftp in text mode. Newlines can be CR, LF or CRLF (Unix, Macintosh or MS-DOS style). 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For more information on notebooks and Mathematica-compatible applications, contact Wolfram Research: web: http://www.wolfram.com email: info@wolfram.com phone: +1-217-398-0700 (U.S.) Notebook reader applications are available free of charge from Wolfram Research. *******************************************************************) (*CacheID: 232*) (*NotebookFileLineBreakTest NotebookFileLineBreakTest*) (*NotebookOptionsPosition[ 20049, 766]*) (*NotebookOutlinePosition[ 20725, 790]*) (* CellTagsIndexPosition[ 20681, 786]*) (*WindowFrame->Normal*) Notebook[{ Cell[CellGroupData[{ Cell["Energie oscillations", "Title"], Cell[CellGroupData[{ Cell["Question 1", "Subsubsection", FormatType->TextForm], Cell[TextData[{ "Une masse ", StyleBox["m", FontSlant->"Italic"], " est attach\[EAcute]e \[AGrave] un ressort et oscille avec une \ p\[EAcute]riode ", StyleBox["T", FontSlant->"Italic"], ". 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La masse vaut ", StyleBox["m", FontSlant->"Italic"], " et la raideur du ressort ", StyleBox["k", FontSlant->"Italic"], ".\na) Quelle est l'\[EAcute]nergie m\[EAcute]canique du syst\[EGrave]me ?\n\ b) Que vaut la vitesse maximale de la masse ?\nc) Quelle est son \ acc\[EAcute]l\[EAcute]ration maximale ?" }], "Text"], Cell[TextData[{ StyleBox["Corrig\[EAcute] 3", FontSlant->"Italic"], "\nL'\[EAcute]nergie m\[EAcute]canique est \[EAcute]gale \[AGrave] l'\ \[EAcute]nergie potentielle \[EAcute]lastique lorsque la masse est immobile. \ Elle s'exprime alors par ", Cell[BoxData[ FormBox[ StyleBox[\(E\_\[EAcute]last\), FontSlant->"Italic"], TextForm]]], "=", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{ StyleBox["k", FontSlant->"Italic"], FormBox[ SuperscriptBox[ StyleBox["A", FontSlant->"Italic"], "2"], "TextForm"]}], "2"], TextForm]]], ". La vitesse maximale est atteinte lorsque la masse passe par sa position \ d'\[EAcute]quilibre. L'\[EAcute]nergie m\[EAcute]canique est alors \ \[EAcute]gale \[AGrave] l'\[EAcute]nergie cin\[EAcute]tique de la masse, ce \ qui permet de trouver ", Cell[BoxData[ FormBox[ StyleBox[\(v\_max\), FontSlant->"Italic"], TextForm]]], "=", Cell[BoxData[ FormBox[ SqrtBox[ StyleBox[\(k\/m\), FontSlant->"Italic"]], TextForm]]], StyleBox["A", FontSlant->"Italic"], ". L'acc\[EAcute]l\[EAcute]ration est maximale lorsque la masse est \ immobile. 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Elle peut donc s'obtenir \ \[AGrave] l'aide de ", Cell[BoxData[ FormBox[ StyleBox[\(E\_tot\), FontSlant->"Italic"], TextForm]]], "=", Cell[BoxData[ FormBox[ StyleBox[\(E\_\[EAcute]last\), FontSlant->"Italic"], TextForm]]], "=", Cell[BoxData[ FormBox[ FractionBox[ RowBox[{ StyleBox["k", FontSlant->"Italic"], FormBox[ SuperscriptBox[ StyleBox["A", FontSlant->"Italic"], "2"], "TextForm"]}], "2"], TextForm]]], ". 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", FontSlant->"Italic"], "Lorsque la vitesse de la particule est \[EAcute]gale \[AGrave] la moiti\ \[EAcute] de la vitesse maximale, son \[EAcute]nergie cin\[EAcute]tique vaut \ ", Cell[BoxData[ FormBox[ StyleBox[\(E\_cin\), FontSlant->"Italic"], TextForm]]], " = ", Cell[BoxData[ FractionBox[ RowBox[{ StyleBox["m", FontSlant->"Italic"], FormBox[ RowBox[{ StyleBox["(", FontSlant->"Italic"], SuperscriptBox[ FormBox[ RowBox[{ FractionBox[ StyleBox[ FormBox[\(v\_max\), "TextForm"], FontSlant->"Italic"], "2"], ")"}], "TextForm"], "2"]}], "TextForm"]}], "2"]]], ".", " La conservation de l'\[EAcute]nergie totale permet d'\[EAcute]crire ", Cell[BoxData[ FormBox[ StyleBox[\(E\_tot\), FontSlant->"Italic"], TextForm]]], "=", Cell[BoxData[ FormBox[ StyleBox[\(E\_cin\), FontSlant->"Italic"], TextForm]]], "+", Cell[BoxData[ FormBox[ StyleBox[\(E\_\[EAcute]last\), FontSlant->"Italic"], TextForm]]], " et de trouver ", StyleBox["x", FontSlant->"Italic"], "=", Cell[BoxData[ FormBox[ FractionBox[ StyleBox[\(\@3\), FontSlant->"Italic"], "2"], TextForm]]], StyleBox["A", FontSlant->"Italic"] }], "Text", FormatType->TextForm], Cell[BoxData[ \(x[A_] := Sqrt[3]/2*A\)], "Input"], Cell[CellGroupData[{ Cell[BoxData[ \(x[0.03]\)], "Input"], Cell[BoxData[ \(0.025980762113533156`\)], "Output"] }, Open ]] }, Open ]], Cell[CellGroupData[{ Cell["Question 6", "Subsubsection", FormatType->TextForm], Cell[TextData[{ "Un syst\[EGrave]me masse-ressort oscille avec une amplitude ", StyleBox["A", FontSlant->"Italic"], ". 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L'\[EAcute]nergie m\[EAcute]canique est alors \ \[EAcute]gale \[AGrave] l'\[EAcute]nergie cin\[EAcute]tique de la masse, ce \ qui permet de trouver ", StyleBox["v", FontSlant->"Italic"], "=", Cell[BoxData[ FormBox[ SqrtBox[ StyleBox[\(k\/m\), FontSlant->"Italic"]], TextForm]]], StyleBox["A", FontSlant->"Italic"], ". L'acc\[EAcute]l\[EAcute]ration est maximale lorsque la masse est \ immobile. 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