// Numbas version: exam_results_page_options
{"name": "Amplitude Modulation", "extensions": ["jsxgraph"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {"eqnline": {"definition": "\nvar div = Numbas.extensions.jsxgraph.makeBoard('400px','400px',\n{boundingBox: [-6,15,6,-15],\n axis: true,\n showNavigation: false,\n grid: true\n});\n  \n// div.board is the object created by JSXGraph, which you use to \n// manipulate elements\nvar board = div.board;  \n\n\n// create the AM wave\nvar AM = board.create('functiongraph',[function(x){return (VDC+Math.cos(x)*Vm)*Math.cos(20*x);}],{strokeColor: 'black', strokeWidth: 1});\nvar envelope1 = board.create('functiongraph',[function(x){return VDC+Math.cos(x)*Vm;}],{strokeColor: 'green', dash: 1, strokeWidth: 1});\nvar envelope2 = board.create('functiongraph',[function(x){return -VDC-Math.cos(x)*Vm;}],{strokeColor: 'red', dash: 1, strokeWidth: 1});var line1 = board.create('line',[[0,VDC],[1,VDC]], { strokeColor: 'red', dash: 3}); \nvar line1 = board.create('line',[[0, VDC],[1, VDC]], { strokeColor: 'blue', dash: 3});\nvar line2 = board.create('line',[[0,-VDC],[1,-VDC]], { strokeColor: 'blue', dash: 3});\n\nreturn div;", "type": "html", "parameters": [["VDC", "number"], ["Vm", "number"]], "language": "javascript"}}, "ungrouped_variables": ["VDC", "VM"], "name": "Amplitude Modulation", "tags": ["graphs", "jsxgraph", "Jsxgraph"], "advice": "<p><img src=\"/question/9060/amplitude-modulation/resources/question-resources/AM_wave.jpg\"/></p>\n<p>The above diagram shows a general AM signal, $v(t) = (V_{DC} + V_m \\cos(2\\pi f_m t))\\cos(2\\pi f_c t)$. The upper envelope is the message signal $V_m \\cos(2\\pi f_m t)$ with an offset of $V_{DC}$, indicated by the dashed red line. Hence, the upper envelope varies between $V_{DC} + V_m$ and $V_{DC} - V_m$, and reading off these values from the AM signal in the question allows us to determine $V_DC$ and $V_m$.</p>", "rulesets": {}, "parts": [{"prompt": "<p>Fill in the gaps with the correct values of VDC and Vm.</p>\n<p>$v(t)=($[[0]]$ +$[[1]] $\\cos(2\\pi f_m t))\\cos(2\\pi f_c t)$</p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "gaps": [{"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "VDC", "minValue": "VDC", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}, {"integerPartialCredit": 0, "integerAnswer": true, "allowFractions": false, "variableReplacements": [], "maxValue": "Vm", "minValue": "Vm", "variableReplacementStrategy": "originalfirst", "correctAnswerFraction": false, "showCorrectAnswer": true, "scripts": {}, "marks": 1, "type": "numberentry", "showPrecisionHint": false}], "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "gapfill"}], "statement": "<p>{eqnline(VDC,Vm)}</p>\n<p>An amplitude modulated carrier defined by the equation $v_s(t) = (V_{DC} + V_m \\cos(2\\pi f_m t))\\cos(2\\pi f_c t)$ is shown above, where $V_{DC}$ is the offset voltage, $V_m$ is the message amplitude, $f_m$ is the message frequency and $f_c$ is the carrier frequency.&nbsp;</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"VDC": {"definition": "random(0..7)", "templateType": "anything", "group": "Ungrouped variables", "name": "VDC", "description": ""}, "VM": {"definition": "random(1..5)", "templateType": "anything", "group": "Ungrouped variables", "name": "VM", "description": ""}}, "metadata": {"notes": "", "description": "<p>This question plots a general amplitude modulated carrier signal defined by $v_s(t) = (V_{DC} + V_m \\cos(2\\pi f_m t))\\cos(2\\pi f_c t)$, where $V_{DC}$ is a DC offset,&nbsp;$V_m$ is the message amplitude, $f_m$ is the message frequency and $f_c$ is the carrier frequency ($f_c = 20f_m$ in this question). The student must identify the values of $V_{DC}$ and $V_m$ and enter these values into the appropriate gaps in the equation of the AM signal.</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Martin Johnston", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/536/"}]}]}], "contributors": [{"name": "Martin Johnston", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/536/"}]}