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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the First Shifting Theorem?
💡 Hint: Think about how exponential functions influence the transforms.
Question 2
Easy
Identify a condition for applying the theorem.
💡 Hint: Check the relationship between s and a.
Practice 4 more questions and get performance evaluation
Interactive Quizzes
Engage in quick quizzes to reinforce what you've learned and check your comprehension.
Question 1
What is the result of applying the First Shifting Theorem to \( f(t) = \sin(b t) \)?
- A. \\( \\mathcal{L}\\{e^{at} sin(bt)\\} = \\frac{b}{(s-a)^2 + b^2} \\)
- B. \\( \\mathcal{L}\\{e^{at} sin(bt)\\} = \\frac{a}{(s+a)^2 + b^2} \\)
- C. \\( \\mathcal{L}\\{e^{at} sin(bt)\\} = \\frac{b}{(s + a)^2 + b^2} \\)
💡 Hint: Recall the basic formula for sin under the shift.
Question 2
True or False: The First Shifting Theorem can only be applied when s > a.
- True
- False
💡 Hint: Consider the implications of the theorem's requirements.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Derive the Laplace Transform of \( e^{0.5t} * t^2 \) using the First Shifting Theorem.
💡 Hint: Start with the basic transform and replace \\( s \\) in the final result.
Question 2
Find a Laplace Transform for \( e^{4t} * an(t) \) using theoretical explanations.
💡 Hint: Consider the behavior of tan in Laplace transforms and apply the theorem correctly.
Challenge and get performance evaluation