// Numbas version: exam_results_page_options
{"name": "FEM 2#1", "extensions": [], "custom_part_types": [], "resources": [["question-resources/3_Springs_RWtq3Yl.jpg", "/srv/numbas/media/question-resources/3_Springs_RWtq3Yl.jpg"], ["question-resources/gsm1.jpg", "/srv/numbas/media/question-resources/gsm1.jpg"], ["question-resources/gsm1_v7hUrSp.jpg", "/srv/numbas/media/question-resources/gsm1_v7hUrSp.jpg"], ["question-resources/fem_b.jpg", "/srv/numbas/media/question-resources/fem_b.jpg"]], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"variables": {"a32": {"group": "Ungrouped variables", "definition": "-k2", "description": "", "name": "a32", "templateType": "anything"}, "a11": {"group": "Ungrouped variables", "definition": "k1", "description": "", "name": "a11", "templateType": "anything"}, "a13": {"group": "Ungrouped variables", "definition": "0", "description": "", "name": "a13", "templateType": "anything"}, "a21": {"group": "Ungrouped variables", "definition": "-k1", "description": "", "name": "a21", "templateType": "anything"}, "a22": {"group": "Ungrouped variables", "definition": "k1+k2", "description": "", "name": "a22", "templateType": "anything"}, "k1": {"group": "Ungrouped variables", "definition": "random(120..250#10)", "description": "", "name": "k1", "templateType": "randrange"}, "a33": {"group": "Ungrouped variables", "definition": "k2", "description": "", "name": "a33", "templateType": "anything"}, "a12": {"group": "Ungrouped variables", "definition": "-k1", "description": "", "name": "a12", "templateType": "anything"}, "f3": {"group": "Ungrouped variables", "definition": "{a32}*{u2}+{a33}*{u}", "description": "", "name": "f3", "templateType": "anything"}, "a23": {"group": "Ungrouped variables", "definition": "-k2", "description": "", "name": "a23", "templateType": "anything"}, "u": {"group": "Ungrouped variables", "definition": "random(1..9#1)", "description": "", "name": "u", "templateType": "randrange"}, "a31": {"group": "Ungrouped variables", "definition": "0", "description": "", "name": "a31", "templateType": "anything"}, "k2": {"group": "Ungrouped variables", "definition": "random(150..210#10)", "description": "", "name": "k2", "templateType": "randrange"}, "u2": {"group": "Ungrouped variables", "definition": "-{a23}*{u}/{a22}", "description": "", "name": "u2", "templateType": "anything"}}, "parts": [{"scripts": {}, "type": "gapfill", "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p style=\"text-align: left; padding-left: 60px;\"><img src=\"resources/question-resources/fem_b.jpg\"/></p>\n<p>First set up&nbsp;the size of the answer matrix (choose the correct number of rows and columns in the boxes) and then input the entries.</p>\n<p style=\"padding-left: 60px;\">\\(\\mathbf A=\\)&nbsp;[[0]]&nbsp;</p>", "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "gaps": [{"allowFractions": false, "tolerance": 0, "markPerCell": true, "correctAnswer": "matrix([\n    [a11,a12,a13],\n    [a21,a22,a23],\n    [a31,a32,a33]\n])", "marks": "4", "variableReplacementStrategy": "originalfirst", "scripts": {}, "showCorrectAnswer": true, "correctAnswerFractions": false, "numRows": "1", "variableReplacements": [], "numColumns": "1", "allowResize": true, "showFeedbackIcon": true, "type": "matrix"}]}, {"scripts": {}, "type": "gapfill", "variableReplacements": [], "showFeedbackIcon": true, "prompt": "<p>Spring 2 is pulled a distance of&nbsp;\\(u_3=\\var{u}\\)mm at node 3 as shown in the diagram.</p>\n<p>Given \\(u_1=0\\), calculate the displacement at node 2 and the force applied to node 3 (<em>F<sub>3</sub></em>).</p>\n<p>Give your answers correct to 3 decimal places.</p>\n<p>\\(u_2=\\)&nbsp;[[0]]mm&nbsp; &nbsp; &nbsp; Give your answer correct to 2 decimal places.</p>\n<p>\\(F_3=\\)&nbsp;[[1]]N/mm&nbsp; &nbsp;Give your answer as an integer.</p>", "variableReplacementStrategy": "originalfirst", "marks": 0, "showCorrectAnswer": true, "gaps": [{"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "scripts": {}, "variableReplacements": [], "marks": 1, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "precisionType": "dp", "precisionPartialCredit": 0, "maxValue": "{u2}", "minValue": "{u2}", "allowFractions": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false, "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "precision": "2", "mustBeReducedPC": 0, "type": "numberentry"}, {"notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "scripts": {}, "variableReplacements": [], "marks": 1, "showPrecisionHint": false, "variableReplacementStrategy": "originalfirst", "correctAnswerStyle": "plain", "precisionType": "dp", "precisionPartialCredit": 0, "maxValue": "{f3}", "minValue": "{f3}", "allowFractions": false, "showCorrectAnswer": true, "showFeedbackIcon": true, "correctAnswerFraction": false, "strictPrecision": false, "precisionMessage": "You have not given your answer to the correct precision.", "precision": "0", "mustBeReducedPC": 0, "type": "numberentry"}]}], "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": ""}, "variable_groups": [], "functions": {}, "variablesTest": {"maxRuns": 100, "condition": ""}, "advice": "<p>The global stiffness matrix is given by:</p>\n<p style=\"padding-left: 30px;\">\\(\\begin{pmatrix} \\var{a11}&amp;\\var{a12}&amp;\\var{a13}\\\\ \\var{a21}&amp;\\var{a22}&amp;\\var{a23}\\\\ \\var{a31}&amp;\\var{a32}&amp;\\var{a33} \\end{pmatrix}\\)</p>\n<p>(b)</p>\n<p style=\"padding-left: 30px;\">\\(\\begin{pmatrix} \\var{a11}&amp;\\var{a12}&amp;\\var{a13}\\\\ \\var{a21}&amp;\\var{a22}&amp;\\var{a23}\\\\ \\var{a31}&amp;\\var{a32}&amp;\\var{a33} \\end{pmatrix}\\begin{pmatrix} u_1\\\\u_2\\\\u_3\\end{pmatrix}=\\begin{pmatrix} F_1\\\\F_2\\\\F_3\\end{pmatrix}\\)</p>\n<p style=\"padding-left: 30px;\">\\(\\begin{pmatrix} \\var{a11}&amp;\\var{a12}&amp;\\var{a13}\\\\ \\var{a21}&amp;\\var{a22}&amp;\\var{a23}\\\\ \\var{a31}&amp;\\var{a32}&amp;\\var{a33} \\end{pmatrix}\\begin{pmatrix} 0\\\\u_2\\\\\\var{u}\\end{pmatrix}=\\begin{pmatrix} F_1\\\\0\\\\F_3\\end{pmatrix}\\)</p>\n<p style=\"padding-left: 30px;\">multiplying out the matrix gives:</p>\n<p style=\"padding-left: 60px;\">\\(0\\var{a12}u_2=F_1\\)</p>\n<p style=\"padding-left: 60px;\">\\(0+\\var{a22}u_2+(\\var{a23})(\\var{u})=0\\)</p>\n<p style=\"padding-left: 90px;\">\\(\\implies u_2=\\simplify{-{a23}*{u}/{a22}}mm\\)</p>\n<p style=\"padding-left: 90px;\">\\(\\implies u_2=\\var{u2}\\)</p>\n<p style=\"padding-left: 60px;\">\\(\\var{a32}u_2+\\var{a33}(\\var{u})=F_3\\)</p>\n<p style=\"padding-left: 90px;\">\\(F_3=\\simplify{{a32}*{u2}+{a33}*{u}}N/mm\\)</p>", "tags": [], "name": "FEM 2#1", "ungrouped_variables": ["k1", "k2", "a11", "a12", "a13", "a21", "a22", "a23", "a31", "a32", "a33", "u", "u2", "f3"], "preamble": {"css": "", "js": ""}, "statement": "<p>Determine the global stiffness matrix for the spring system below, where</p>\n<p>&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp;&nbsp; k<sub>1</sub> =&nbsp;\\(\\var{k1}N/mm\\),&nbsp;&nbsp;&nbsp; k<sub>2</sub> = \\(\\var{k2}N/mm\\).</p>", "extensions": [], "rulesets": {}, "type": "question", "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}]}], "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}]}