See 'show steps'.
", "rulesets": {}, "parts": [{"stepsPenalty": 0, "variableReplacements": [], "prompt": "Find $L\\{\\var{a} \\}$.
", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "$L\\{k\\}=\\frac{k}{s}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "{a}/s", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"stepsPenalty": 0, "variableReplacements": [], "prompt": "Find $L\\{\\var{b}t \\}$.
", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "$L\\{t\\}=\\frac{1}{s^2}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "{b}/s^2", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"stepsPenalty": 0, "variableReplacements": [], "prompt": "Find $L\\{\\var{a}+\\var{b}t \\}$.
", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "$L\\{k\\}=\\frac{k}{s}$
\n$L\\{t\\}=\\frac{1}{s^2}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "{a}/s+{b}/s^2", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"stepsPenalty": 0, "variableReplacements": [], "prompt": "Find $L\\{t^\\var{a}\\}$.
", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "$L\\{t^n\\}=\\frac{n!}{s^{n+1}}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "fact({a})/s^{a+1}", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"stepsPenalty": 0, "variableReplacements": [], "prompt": "Find $L\\{\\var{a}t^\\var{c}+\\var{b}t^\\var{d}\\}$.
", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "$L\\{t^n\\}=\\frac{n!}{s^{n+1}}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "({a}*(fact({c})))/s^{c+1}+({b}*(fact({d})))/s^{d+1}", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "statement": "You may use a table of Laplace transforms in order to answer the following questions.
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(1..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random(2..5#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(6..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "Laplace of constants and powers of t
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", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Laplace of e^(at)", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "c", "b", "d"], "tags": ["rebelmaths"], "preamble": {"css": "", "js": ""}, "advice": "(a) Using the tables, $L[e^{\\var{a}t}]=\\frac{1}{s-\\var{a}}$
\n(b) Using the tables, $L[e^{\\var{b}t}]=\\frac{1}{s-(\\var{b})}$
\n(c) Using the tables, $L[e^{\\var{c}t}+e^{\\var{d}t}]=\\frac{1}{s-(\\var{c})}+\\frac{1}{s-\\var{d}}$
", "rulesets": {}, "parts": [{"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "Find the laplace transform of $e^{\\var{a}t}$
", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Note that the Laplace transform of $e^{at}$ is $\\frac{1}{s-a}$
\n$L\\{e^{at}\\}=\\frac{1}{s-a}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "1/(s-{a})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "Find the laplace transform of $e^{\\var{b}t}$
", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Note that the Laplace transform of $e^{at}$ is $\\frac{1}{s-a}$
\n$L\\{e^{at}\\}=\\frac{1}{s-a}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "1/(s-{b})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}, {"stepsPenalty": 0, "vsetrangepoints": 5, "prompt": "Find the laplace transform of $ { e^{ \\var{c} t}+e^{ \\var{d} t} }$
\n", "expectedvariablenames": [], "checkingaccuracy": 0.001, "vsetrange": [0, 1], "showpreview": true, "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "When you have the Laplace transform of two functions added together you just get the Laplace transform of each function and add the two answers.
\n$L\\{f(t)+g(t)\\}=L\\{f(t)\\}+L\\{g(t)\\}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "showCorrectAnswer": true, "scripts": {}, "answer": "1/(s-{c})+1/(s-{d})", "marks": 1, "checkvariablenames": false, "checkingtype": "absdiff", "type": "jme"}], "statement": "You may use a table of Laplace transforms in order to answer the following questions.
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "variables": {"a": {"definition": "random (2..9 except [0,1])", "templateType": "anything", "group": "Ungrouped variables", "name": "a", "description": ""}, "c": {"definition": "random (-9..-2 except [0,1,-1])", "templateType": "anything", "group": "Ungrouped variables", "name": "c", "description": ""}, "b": {"definition": "random (-9..-2)", "templateType": "anything", "group": "Ungrouped variables", "name": "b", "description": ""}, "d": {"definition": "random (-9..9 except [0,1,-1])", "templateType": "anything", "group": "Ungrouped variables", "name": "d", "description": ""}}, "metadata": {"description": "Laplace transform of e^{at}
\nrebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Laplace of trig functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Julie Crowley", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/113/"}], "functions": {}, "ungrouped_variables": ["a", "b"], "tags": ["rebelmaths"], "advice": "See 'show steps'.
", "rulesets": {}, "parts": [{"stepsPenalty": 0, "variableReplacements": [], "prompt": "Find $L\\{\\cos(\\var{a}t)\\}$
\n", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Note: $L\\{\\cos(bt)\\}=\\frac{s}{s^2+b^2}$
\nIn this example $b=\\var{a}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "s/(s^2+{a}^2)", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"stepsPenalty": 0, "variableReplacements": [], "prompt": "Find $L\\{\\sin(\\var{b}t)\\}$
", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Note: $L\\{\\sin(bt)\\}=\\frac{b}{s^2+b^2}$
\nIn this example $b=\\var{b}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "{b}/(s^2+{b}^2)", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}, {"stepsPenalty": 0, "variableReplacements": [], "prompt": "Find $L\\{\\cos(\\frac{t}{\\var{a}})+\\sin(\\frac{t}{\\var{b}})\\}$
\n", "expectedvariablenames": [], "checkingaccuracy": 0.001, "type": "jme", "showpreview": true, "vsetrangepoints": 5, "variableReplacementStrategy": "originalfirst", "steps": [{"prompt": "Note: $L\\{\\cos(bt)\\}=\\frac{s}{s^2+b^2}$ and $L\\{\\sin(bt)\\}=\\frac{b}{s^2+b^2}$
\nIn the first part $b=\\frac{1}{\\var{a}}$ and in the second part $b=\\frac{1}{\\var{b}}$
", "variableReplacements": [], "variableReplacementStrategy": "originalfirst", "showCorrectAnswer": true, "scripts": {}, "marks": 0, "type": "information"}], "marks": 1, "scripts": {}, "answer": "s/(s^2+{1/a}^2)+{1/b}/(s^2+{1/b}^2)", "showCorrectAnswer": true, "checkvariablenames": false, "checkingtype": "absdiff", "vsetrange": [0, 1]}], "statement": "You may use a table of Laplace transforms in order to answer the following questions.
", "variable_groups": [], "variablesTest": {"maxRuns": 100, "condition": ""}, "preamble": {"css": "", "js": ""}, "variables": {"a": {"definition": "random(2..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "a", "description": ""}, "b": {"definition": "random(2..9#1)", "templateType": "randrange", "group": "Ungrouped variables", "name": "b", "description": ""}}, "metadata": {"description": "rebelmaths
", "licence": "Creative Commons Attribution 4.0 International"}, "type": "question", "showQuestionGroupNames": false, "question_groups": [{"name": "", "pickingStrategy": "all-ordered", "pickQuestions": 0, "questions": []}]}, {"name": "Laplace transform #1 - powers of t and exp", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Chris Graham", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/369/"}, {"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "tags": [], "functions": {}, "advice": "", "variable_groups": [], "variables": {"k": {"description": "", "definition": "random(2 .. 12#0.5)", "name": "k", "templateType": "randrange", "group": "Ungrouped variables"}, "n": {"description": "", "definition": "random(2 .. 5#1)", "name": "n", "templateType": "randrange", "group": "Ungrouped variables"}, "b": {"description": "", "definition": "random(2 .. 11#1)", "name": "b", "templateType": "randrange", "group": "Ungrouped variables"}, "a": {"description": "", "definition": "random(2 .. 10#1)", "name": "a", "templateType": "randrange", "group": "Ungrouped variables"}}, "preamble": {"css": "", "js": ""}, "ungrouped_variables": ["a", "b", "k", "n"], "statement": "What is the Laplace transform for the function:
\n\\(x(t)=\\var{a}t^{\\var{n}}+\\var{b}e^{-\\var{k}t}.\\)
\n", "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "rulesets": {}, "parts": [{"customMarkingAlgorithm": "", "marks": 0, "customName": "", "variableReplacementStrategy": "originalfirst", "useCustomName": false, "prompt": "\\(X(s)=\\) [[0]]
", "sortAnswers": false, "type": "gapfill", "gaps": [{"customMarkingAlgorithm": "", "marks": 1, "customName": "", "checkVariableNames": false, "showPreview": true, "variableReplacementStrategy": "originalfirst", "checkingType": "absdiff", "valuegenerators": [{"value": "", "name": "s"}], "useCustomName": false, "failureRate": 1, "vsetRangePoints": 5, "answer": "fact{n}*{a}/s^{n+1}+{b}/(s+{k})", "checkingAccuracy": 0.001, "type": "jme", "vsetRange": [0, 1], "scripts": {}, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true}], "scripts": {}, "unitTests": [], "showCorrectAnswer": true, "showFeedbackIcon": true, "variableReplacements": [], "extendBaseMarkingAlgorithm": true}], "variablesTest": {"condition": "", "maxRuns": 100}}, {"name": "Laplace transform #2 - Trig functions", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "metadata": {"description": "", "licence": "Creative Commons Attribution-NonCommercial 4.0 International"}, "statement": "What is the Laplace transform for the function:
\n\\(x(t)=\\var{a}sin({\\var{n}t})+\\var{b}cos({\\var{k}t}).\\)
\n", "functions": {}, "preamble": {"css": "", "js": ""}, "tags": [], "parts": [{"showCorrectAnswer": true, "prompt": "\\(X(s)=\\) [[0]]
", "scripts": {}, "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 0, "type": "gapfill", "gaps": [{"showCorrectAnswer": true, "answer": "{n}*{a}/(s^2+{n}^2)+{b}s/(s^2+{k}^2)", "failureRate": 1, "scripts": {}, "vsetRange": [0, 1], "vsetRangePoints": 5, "checkVariableNames": false, "extendBaseMarkingAlgorithm": true, "variableReplacementStrategy": "originalfirst", "showFeedbackIcon": true, "marks": 1, "checkingAccuracy": 0.001, "type": "jme", "checkingType": "absdiff", "customMarkingAlgorithm": "", "variableReplacements": [], "expectedVariableNames": [], "unitTests": [], "showPreview": true}], "customMarkingAlgorithm": "", "variableReplacements": [], "unitTests": []}], "advice": "", "variables": {"n": {"templateType": "randrange", "description": "", "definition": "random(2..5#1)", "group": "Ungrouped variables", "name": "n"}, "k": {"templateType": "randrange", "description": "", "definition": "random(2..12#1)", "group": "Ungrouped variables", "name": "k"}, "b": {"templateType": "randrange", "description": "", "definition": "random(2..11#1)", "group": "Ungrouped variables", "name": "b"}, "a": {"templateType": "randrange", "description": "", "definition": "random(2..10#1)", "group": "Ungrouped variables", "name": "a"}}, "ungrouped_variables": ["a", "b", "k", "n"], "variablesTest": {"condition": "", "maxRuns": 100}, "rulesets": {}, "variable_groups": [], "type": "question"}, {"name": "Laplace transform #3 - powers of t by exp", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "variables": {"n": {"definition": "random(2..5#1)", "name": "n", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "b": {"definition": "random(2..11#1)", "name": "b", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "k": {"definition": "random(2..12#0.5)", "name": "k", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "a": {"definition": "random(2..10#1)", "name": "a", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}}, "advice": "", "variable_groups": [], "statement": "What is the Laplace transform for the function:
\n\\(x(t)=\\var{a}t^{\\var{n}}e^{-\\var{k}t}+\\var{b}.\\)
\n", "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"scripts": {}, "type": "gapfill", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "marks": 0, "gaps": [{"checkingAccuracy": 0.001, "scripts": {}, "type": "jme", "failureRate": 1, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "vsetRange": [0, 1], "showPreview": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "marks": 1, "vsetRangePoints": 5, "answer": "fact{n}*{a}/(s+{k})^{n+1}+{b}/s"}], "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "prompt": "\\(X(s)=\\) [[0]]
"}], "rulesets": {}, "ungrouped_variables": ["a", "b", "k", "n"], "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": ""}, "type": "question"}, {"name": "Find the Laplace transform of ode", "extensions": [], "custom_part_types": [], "resources": [], "navigation": {"allowregen": true, "showfrontpage": false, "preventleave": false, "typeendtoleave": false}, "contributors": [{"name": "Frank Doheny", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/789/"}, {"name": "Marie Nicholson", "profile_url": "https://numbas.mathcentre.ac.uk/accounts/profile/1799/"}], "variables": {"d": {"definition": "random(3..8#1)", "name": "d", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "b": {"definition": "random(10..25#1)", "name": "b", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "g": {"definition": "random(3..9#1)", "name": "g", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "a": {"definition": "random(2..10#1)", "name": "a", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "f": {"definition": "random(1..6#1)", "name": "f", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}, "c": {"definition": "random(3..12#1)", "name": "c", "group": "Ungrouped variables", "templateType": "randrange", "description": ""}}, "advice": "\\(\\frac{d^2x}{dt^2}+\\var{a}\\frac{dx}{dt}+\\var{b}x(t)=\\var{c}e^{-\\var{d}t}\\) where \\(x(0)=\\var{f}\\) and \\(x'(0)=\\var{g}\\)
\n\n\\(s^2X(s)-sx(0)-x'(0)+\\var{a}(s(X(s)-x(0))+\\var{b}X(s)=\\frac{\\var{c}}{s+\\var{d}}\\)
\n\n\\(s^2X(s)-\\var{f}s-\\var{g}+\\var{a}sX(s)-\\var{a}*\\var{f}+\\var{b}X(s)=\\frac{\\var{c}}{s+\\var{d}}\\)
\n\n\\(s^2X(s)+\\var{a}sX(s)+\\var{b}X(s)=\\frac{\\var{c}}{s+\\var{d}}+\\var{f}s+\\simplify{{g}+{a}*{f}}\\)
\n\n\\((s^2+\\var{a}s+\\var{b})X(s)=\\frac{\\var{c}+(\\var{f}s+\\simplify{{g}+{a}*{f}})(s+\\var{d})}{s+\\var{d}}\\)
\n\n\\(X(s)=\\frac{\\simplify{{f}s^2+({a}*{f}+{g}+{d}*{f})s+(({g}+{f}*{a})*{d}+{c})}}{(s+\\var{d})(s^2+\\var{a}s+\\var{b})}\\)
\n.
", "variable_groups": [], "statement": "Find the Laplace transform of the following differential equation and express it as a single fraction:
\n\\(\\frac{d^2x}{dt^2}+\\var{a}\\frac{dx}{dt}+\\var{b}x(t)=\\var{c}e^{-\\var{d}t}\\) where \\(x(0)=\\var{f}\\) and \\(x'(0)=\\var{g}\\)
", "functions": {}, "preamble": {"css": "", "js": ""}, "variablesTest": {"maxRuns": 100, "condition": ""}, "parts": [{"scripts": {}, "type": "gapfill", "sortAnswers": false, "extendBaseMarkingAlgorithm": true, "marks": 0, "gaps": [{"checkingAccuracy": 0.001, "scripts": {}, "type": "jme", "failureRate": 1, "checkingType": "absdiff", "extendBaseMarkingAlgorithm": true, "expectedVariableNames": [], "checkVariableNames": false, "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "vsetRange": [0, 1], "showPreview": true, "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "marks": "3", "vsetRangePoints": 5, "answer": "({f}s^2+({f}*{a}+{g}+{d}*{f})s+(({g}+{a}*{f})*{d}+{c}))/((s+{d})(s^2+{a}s}+{b}))"}], "unitTests": [], "showFeedbackIcon": true, "variableReplacements": [], "showCorrectAnswer": true, "customMarkingAlgorithm": "", "variableReplacementStrategy": "originalfirst", "prompt": "\\(X(s)=\\) [[0]]
"}], "rulesets": {}, "ungrouped_variables": ["a", "b", "c", "d", "f", "g"], "tags": [], "metadata": {"licence": "Creative Commons Attribution-NonCommercial 4.0 International", "description": ""}, "type": "question"}]}], "showstudentname": true, "duration": 0, "navigation": {"showresultspage": "oncompletion", "showfrontpage": false, "onleave": {"action": "none", "message": ""}, "reverse": true, "preventleave": true, "browse": true, "allowregen": true}, "metadata": {"description": "Laplace from tables: e^(at), cos(bt), sin(bt).
\nrebelmaths
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\n1. Try a question.
\n2. If you do not get full marks on the question
\n3. If you get full marks on the question proceed to next question.
\nEnjoy!
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