// Numbas version: exam_results_page_options
{"name": "Shifted Simple Harmonic Motion Graph", "extensions": ["geogebra"], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"extensions": ["geogebra"], "tags": [], "metadata": {"licence": "Creative Commons Attribution 4.0 International", "description": "<p>This uses an embedded Geogebra SHM graph with coefficients set by NUMBAS.</p>"}, "ungrouped_variables": ["defs", "a", "b", "w", "hmin", "hmax"], "statement": "<p>The depth of water, $h$ metres, of a harbour at time $t$ hours, can be modelled as simple harmonic motion about a fixed depth.</p>\n<p>{geogebra_applet('https://ggbm.at/njwfpvb7', defs, [])}</p>", "variablesTest": {"condition": "hmin>1 and hmax<16 and a<>b", "maxRuns": "200"}, "variable_groups": [], "parts": [{"showCorrectAnswer": true, "prompt": "<p>SHM origin, $h = $&nbsp;[[0]] metres</p>\n<p>Maximum depth, $h_{max} = $&nbsp;[[1]] metres</p>\n<p>Minimum depth, $h_{min} = $&nbsp;[[2]] metres</p>", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false, "type": "gapfill", "scripts": {}, "marks": 0, "unitTests": [], "gaps": [{"showCorrectAnswer": true, "minValue": "{b}", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": true, "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "unitTests": [], "maxValue": "{b}", "notationStyles": ["plain", "en", "si-en"], "allowFractions": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}, {"showCorrectAnswer": true, "minValue": "{hmax}", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": true, "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "unitTests": [], "maxValue": "{hmax}", "notationStyles": ["plain", "en", "si-en"], "allowFractions": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}, {"showCorrectAnswer": true, "minValue": "{hmin}", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "mustBeReducedPC": 0, "type": "numberentry", "mustBeReduced": false, "correctAnswerFraction": true, "scripts": {}, "marks": 1, "correctAnswerStyle": "plain", "unitTests": [], "maxValue": "{hmin}", "notationStyles": ["plain", "en", "si-en"], "allowFractions": true, "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}, {"showCorrectAnswer": true, "matrix": ["2", 0, 0, 0], "prompt": "<p>Which of the following best describes the depth of water after $t$ hours?</p>\n<p></p>", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "type": "1_n_2", "showCellAnswerState": true, "shuffleChoices": true, "scripts": {}, "marks": 0, "maxMarks": 0, "displayColumns": 0, "unitTests": [], "distractors": ["", "", "", ""], "displayType": "radiogroup", "minMarks": 0, "choices": ["$h=\\var{a}\\sin \\omega t + \\var{b}$", "$h=\\var{a}\\cos\\omega t + \\var{b}$", "$h=\\var{b}\\sin \\omega t + \\var{a}$", "$h=\\var{b}\\cos \\omega t + \\var{a}$"], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}, {"showCorrectAnswer": true, "prompt": "<p>There are two high tides in a 25 hour period.&nbsp; Calculate the angular frequency for the harbour depth:</p>\n<p>Angular frequency, $\\omega = $&nbsp;[[0]] rad/hour</p>", "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "sortAnswers": false, "type": "gapfill", "scripts": {}, "marks": 0, "unitTests": [], "gaps": [{"showCorrectAnswer": true, "expectedVariableNames": [], "showPreview": true, "variableReplacementStrategy": "originalfirst", "customMarkingAlgorithm": "", "type": "jme", "checkingAccuracy": 0.001, "answer": "4pi/25", "checkVariableNames": false, "failureRate": 1, "scripts": {}, "marks": "2", "vsetRange": [0, 1], "unitTests": [], "answerSimplification": "all", "vsetRangePoints": 5, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}], "extendBaseMarkingAlgorithm": true, "variableReplacements": [], "showFeedbackIcon": true}], "name": "Shifted Simple Harmonic Motion Graph", "rulesets": {}, "functions": {"graph": {"type": "html", "language": "jme", "definition": "", "parameters": []}}, "preamble": {"js": "", "css": ""}, "variables": {"w": {"definition": "4pi/25", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "w"}, "a": {"definition": "random(2..10)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "a"}, "hmax": {"definition": "b+a", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "hmax"}, "hmin": {"definition": "b-a", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "hmin"}, "defs": {"definition": "[\n  ['a',a],\n  ['b',b]\n]", "group": "Ungrouped variables", "templateType": "anything", "description": "<p>Sets the internal values of y = a*cos(wx+c)+d</p>", "name": "defs"}, "b": {"definition": "random(1..10)", "group": "Ungrouped variables", "templateType": "anything", "description": "", "name": "b"}}, "advice": "<p></p>\n<p>(c) Two high-tides in 25 hours means the period is half of that value:&nbsp; 1 high tide per 12.5 hours. Therefore \\[ P = 12.5 \\text{ hours} \\] Angular frequency, $\\omega$, is defined as \\[ \\omega = \\frac{2\\pi}{12.5} =\\frac{4\\pi}{25} \\, \\mathrm{rad/hr} \\] where $P$ is the period of oscillation.</p>", "type": "question", "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}]}], "contributors": [{"name": "Adrian Jannetta", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/164/"}]}