Introduction to Laplace Transforms
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\n$L\\{t\\}=\\frac{1}{s^2}$
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", "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.
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\n(b) Using the tables, $L[e^{\\var{b}t}]=\\frac{1}{s-(\\var{b})}$
\n(c) Using the tables, $L[e^{\\var{c}t}+e^{\\var{d}t}]=\\frac{1}{s-(\\var{c})}+\\frac{1}{s-\\var{d}}$
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\n$L\\{e^{at}\\}=\\frac{1}{s-a}$
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\n$L\\{e^{at}\\}=\\frac{1}{s-a}$
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\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$L\\{f(t)+g(t)\\}=L\\{f(t)\\}+L\\{g(t)\\}$
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\nIn this example $b=\\var{a}$
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\nIn this example $b=\\var{b}$
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\nIn the first part $b=\\frac{1}{\\var{a}}$ and in the second part $b=\\frac{1}{\\var{b}}$
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"}}, "feedback": {"showactualmark": true, "showtotalmark": true, "showanswerstate": true, "allowrevealanswer": true, "advicethreshold": 0, "intro": "This test is on simple Laplace transforms. It will reward those of you who have attended and completed Journal 3 with an easy 3% for this module. For those of you who have not attended and are a little behind, this test should hopefully help you grasp the basics now and earn you 3% whilst doing it.
\nYou have 30 minutes to complete this test. You may pause it, and you may reveal answers for help and regenerate another question to attempt.
\nAs usual once you have scored full marks DO NOT ENTER the test again as this will wipe your grade.
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