18.2.3 - Step 3: Apply the inverse Laplace Transform to find π(π‘)
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Practice Questions
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What is the purpose of the inverse Laplace Transform?
π‘ Hint: Think about what we want to achieve with the function after using Laplace Transform.
Define a Volterra Integral Equation.
π‘ Hint: Consider the form of integral equations we discussed.
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Interactive Quizzes
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What does the inverse Laplace Transform retrieve?
π‘ Hint: Consider what you ultimately want to find in function analysis.
True or False: The Laplace Transform can simplify integral equations to algebraic equations.
π‘ Hint: Recall how we use Laplace in engineering applications.
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Challenge Problems
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Given πΉ(π ) = 1 / (sΒ² + 9), find the inverse Laplace Transform and express π(π‘).
π‘ Hint: Look for trigonometric forms in your inverse Laplace Transform tables.
Consider the equation π(π‘) = 1 + β« (t - Ο)f(Ο)dΟ. Solve for π(π‘) by following the steps of Laplace and inverse.
π‘ Hint: Follow the structured steps of the Laplace Transform to derive the equation and solve.
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