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{"name": "Transfer function from differential equation", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"parts": [{"useCustomName": false, "adaptiveMarkingPenalty": 0, "showFeedbackIcon": true, "customName": "", "customMarkingAlgorithm": "", "variableReplacements": [], "gaps": [{"useCustomName": false, "scripts": {}, "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "maxValue": "{a_2}", "correctAnswerFraction": false, "marks": "0.5", "customName": "", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "customMarkingAlgorithm": "", "minValue": "{a_2}", "correctAnswerStyle": "plain"}, {"useCustomName": false, "scripts": {}, "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "maxValue": "{a_1}", "correctAnswerFraction": false, "marks": "0.5", "customName": "", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "customMarkingAlgorithm": "", "minValue": "{a_1}", "correctAnswerStyle": "plain"}, {"useCustomName": false, "scripts": {}, "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "maxValue": "{a_0}", "correctAnswerFraction": false, "marks": "0.5", "customName": "", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "customMarkingAlgorithm": "", "minValue": "{a_0}", "correctAnswerStyle": "plain"}, {"useCustomName": false, "scripts": {}, "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "maxValue": "-{b_2}", "correctAnswerFraction": false, "marks": "0.5", "customName": "", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "customMarkingAlgorithm": "", "minValue": "-{b_2}", "correctAnswerStyle": "plain"}, {"useCustomName": false, "scripts": {}, "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "maxValue": "-{b_1}", "correctAnswerFraction": false, "marks": "0.5", "customName": "", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "customMarkingAlgorithm": "", "minValue": "-{b_1}", "correctAnswerStyle": "plain"}, {"useCustomName": false, "scripts": {}, "type": "numberentry", "variableReplacements": [], "showFeedbackIcon": true, "maxValue": "-{b_0}", "correctAnswerFraction": false, "marks": "0.5", "customName": "", "allowFractions": false, "extendBaseMarkingAlgorithm": true, "notationStyles": ["plain", "en", "si-en"], "mustBeReduced": false, "adaptiveMarkingPenalty": 0, "mustBeReducedPC": 0, "showCorrectAnswer": true, "showFractionHint": true, "variableReplacementStrategy": "originalfirst", "unitTests": [], "customMarkingAlgorithm": "", "minValue": "-{b_0}", "correctAnswerStyle": "plain"}], "showCorrectAnswer": true, "sortAnswers": false, "prompt": "<p>The system is described by the following differential equation:</p>\n<p>\\[{\\var{a_2}}\\frac{d^2y}{dt^2} + ({\\var{a_1}})\\frac{dy}{dt}+(\\var{a_0})y+(\\var{b_2})\\frac{d^2u}{dt^2}+(\\var{b_1})\\frac{du}{dt}+(\\var{b_0})u=0\\]</p>\n<p>The transfer function is given by \\[\\frac{Y(s)}{U(s)} = \\frac{b_2s^2+b_1s+b_0}{a_2s^2+a_1s+a_0}\\]</p>\n<p>\\(b_2 = \\)[[3]] \\(b_1 = \\)[[4]] \\(b_0 = \\)[[5]]</p>\n<p>\\(a_2 = \\)[[0]] \\(a_1 = \\)[[1]] \\(a_0 = \\)[[2]]</p>\n<p></p>", "marks": 0, "unitTests": [], "scripts": {}, "type": "gapfill", "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst"}], "rulesets": {}, "functions": {}, "metadata": {"licence": "Creative Commons Attribution-ShareAlike 4.0 International", "description": "This question tests the students skill on transfer functions and Laplace of differential equations. The coefficients of the functions are created randomly.<br>"}, "extensions": [], "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "statement": "<p>Find the transfer function of the following differential equation by taking the Laplace transform.</p>", "ungrouped_variables": ["b_2", "b_1", "b_0", "a_2", "a_1", "a_0"], "advice": "", "preamble": {"css": "", "js": ""}, "tags": ["control theory", "cybernetics", "differential equations", "Differential equations", "laplace"], "variables": {"b_1": {"definition": "random(-30 .. 30#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "b_1"}, "a_2": {"definition": "random(-15 .. 15#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "a_2"}, "a_0": {"definition": "random(-100 .. 100#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "a_0"}, "b_0": {"definition": "random(-50 .. 50#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "b_0"}, "a_1": {"definition": "random(-50 .. 50#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "a_1"}, "b_2": {"definition": "random(-10 .. 10#1)", "group": "Ungrouped variables", "description": "", "templateType": "randrange", "name": "b_2"}}, "name": "Transfer function from differential equation", "contributors": [{"name": "Aleksander Skrede", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3744/"}, {"name": "Robin T. Bye", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3758/"}]}]}], "contributors": [{"name": "Aleksander Skrede", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3744/"}, {"name": "Robin T. Bye", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/3758/"}]}