Practice Meaning - 1.5 | 3. Topic 3: First Shifting Theorem | Mathematics - iii (Differential Calculus) - Vol 1
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Meaning

1.5 - Meaning

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Practice Questions

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Question 1 Easy

Apply the First Shifting Theorem on f(t) = t. What do you get?

💡 Hint: Remember to shift s to s-a when using the theorem.

Question 2 Easy

What is the Laplace Transform of e^2t when f(t) is 1?

💡 Hint: Consider the basic Laplace Transform for constant functions.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What does the First Shifting Theorem state?

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

💡 Hint: Recall the specific application of the exponential multiplication.

Question 2

True or False: If f(t) has an exponential growth term, you will always apply shifting to the right.

True
False

💡 Hint: Consider how the signs of a and e influence the shift.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Create a situation where you have a mechanical system modeled by e^{-3t}t. Find its Laplace Transform and explain your reasoning.

💡 Hint: Recognize how the exponential affects the time variable.

Challenge 2 Hard

Justify the importance of confirming s > Re(a) in practical engineering applications.

💡 Hint: Think about the implications of growth rates.

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