Practice Transform Of Shifted Functions (15.12.2) - Fourier Integral to Laplace Transforms
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Transform of Shifted Functions

Practice - Transform of Shifted Functions

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define a shifted function in your own words.

💡 Hint: Think about when you add something to a system.

Question 2 Easy

What is the purpose of the unit step function in shifted functions?

💡 Hint: Consider how the function behaves before and after the delay.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the formula for the Laplace transform of a shifted function?

L{f(t-a)u(t-a)} = e^{-as}F(s)
L{f(t+a)u(t+a)} = e^{as}F(s)
L{f(t-u(t-a))} = F(s)

💡 Hint: Focus on how the shift modifies the standard Laplace transformation.

Question 2

True or False: The unit step function allows a function to begin analysis at t<0.

True
False

💡 Hint: Remember the definition of the unit step function.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

A system experiences a load that starts fluctuating after 4 seconds. If the function describing load fluctuation is f(t) = sin(t), express its Laplace transform and explain the significance of transformations in engineering.

💡 Hint: Reflect on how you account for the shift when applying the transform.

Challenge 2 Hard

Model a scenario where material is added to a structure 5 seconds after construction begins. Define the function and calculate its Laplace transform.

💡 Hint: Break down the process into defining the load before transforming.

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