Practice Laplace Transform Of Piecewise And Discontinuous Functions (15.12) - Fourier Integral to Laplace Transforms

Practice: Laplace Transform of Piecewise and Discontinuous Functions

Lesson 15.12Fourier Integral to Laplace Transforms

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9 questions

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6 sample questions

Question 1.
Define a unit step function.
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Think about how the function reacts before and after a certain time.
Question 2.
What is the transform of the unit step function?
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Recall the equation we just discussed.
3Question 3.
What is the Laplace Transform of the unit step function?
- e^{-as}/s
- s/e^{as}
- 0
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Remember the definition of the unit step function.
4Question 4.
True or False: The shifted function allows for effective modeling of loads applied after a delay.
- True
- False
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Think about when a load starts acting.
Question 5.
Given a beam subjected to a point load that is instantly applied at t=3s and removed at t=6s, represent the load using a piecewise function and find its Laplace transform.
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Look into how each piece of the load behaves at different times.
Question 6.
Formulate and solve for the Laplace transform of the following piecewise function: f(t) = 10u(t-2) + 5u(t-4).
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Break it down by examining each unit step function's contribution.

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