Practice Inverse Laplace Transform (15.8) - Fourier Integral to Laplace Transforms

Practice: Inverse Laplace Transform

Lesson 15.8Fourier Integral to Laplace Transforms

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9 questions

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6 sample questions

Question 1.
What does the Inverse Laplace Transform retrieve?
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Think about what the 'inverse' implies in mathematics.
Question 2.
State the notation for the Inverse Laplace Transform.
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It starts with 'L' for Laplace.
3Question 3.
What does the Inverse Laplace Transform do?
- Converts time functions to Laplace domain
- Retrieves the time-domain function from its Laplace transform
- Finds the derivative of a function
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Consider what 'inverse' means in mathematical operations.
4Question 4.
True or False: Partial Fraction Decomposition is not needed when finding the inverse Laplace transform.
- True
- False
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Think about why we simplify before transformations.
Question 5.
A system's response is described by F(s) = (3s + 7)/(s^2 + 4). Find f(t) using inverse Laplace transform techniques.
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Look at the standard forms for sine and cosine.
Question 6.
Given F(s) = e^(-3s)/(s + 2), what does f(t) equal? Explain each step of your reasoning.
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Remember how e^(-as) relates to the unit step function for shifts.

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