// Numbas version: finer_feedback_settings
{"name": "Inverse Laplace  - trig functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "question_groups": [{"pickingStrategy": "all-ordered", "questions": [{"functions": {}, "ungrouped_variables": ["a", "c", "b", "d"], "name": "Inverse Laplace  - trig functions", "tags": [], "preamble": {"css": "", "js": ""}, "advice": "<p>See 'show steps'.</p>", "rulesets": {}, "parts": [{"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "<p>Find $L^{-1}\\{\\frac{s}{s^2+{\\var{a}}^2}\\}$</p>\n<p></p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Note: $L\\{\\cos(bt)\\}=\\frac{s}{s^2+b^2}$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "cos({a}t)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "<p>Find $L^{-1}\\{ \\frac {\\var{b}} {s^2+\\var{b}^2}\\}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "<p>Note: $L\\{\\sin(bt)\\}=\\frac{b}{s^2+b^2}$</p>\n<p></p>", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "sin({b}t)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "<p>Find $L^{-1}\\{\\frac{\\var{c}s}{s^2+\\var{a}}\\}$.</p>\n<p></p>\n<p>Note to input $\\sqrt{x}$, type sqrt(x).</p>\n<p></p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "{c}*cos(sqrt({a})t)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"vsetrangepoints": 5, "prompt": "<p>Find $L^{-1}\\{\\frac{{\\var{d}}}{s^2+\\var{b}^2}\\}$</p>", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "answer": "{d}/{b}sin({b}t)", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "extensions": [], "statement": "<p>You may use a table of Laplace transforms in order to answer the following questions.</p>", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random(2..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random(2..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random(2..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "<p>Inverse Laplace transform if trig functions.</p>\n<p>Rebelmaths</p>", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}]}], "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}]}