Practice First Shifting Theorem - 15.7.2 | 15. Fourier Integral to Laplace Transforms | Mathematics (Civil Engineering -1)
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First Shifting Theorem

15.7.2 - First Shifting Theorem

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Practice Questions

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Question 1 Easy

What is the First Shifting Theorem?

💡 Hint: Think about how the Laplace transform changes with exponential functions.

Question 2 Easy

If f(t) = cos(t), how would you express L{e^{5t}cos(t)}?

💡 Hint: Remember to identify the original function before applying the theorem.

4 more questions available

Interactive Quizzes

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Question 1

What does the First Shifting Theorem state?

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

💡 Hint: Focus on the relationship between exponential and Laplace transforms.

Question 2

True or False: The First Shifting Theorem is used solely in theoretical mathematics.

True
False

💡 Hint: Think about where Laplace transforms are applied.

1 more question available

Challenge Problems

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Challenge 1 Hard

Apply the First Shifting Theorem to the function f(t) = e^{4t} * t^3 and find its Laplace transform.

💡 Hint: Calculate the basic Laplace transform first.

Challenge 2 Hard

Explain how the First Shifting Theorem applies when analyzing a damped harmonic oscillator with an exponential decay factor added.

💡 Hint: Consider how damping impacts frequency responses.

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