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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Find the Laplace Transform of e^3t * cos(5t).
💡 Hint: Start with the transform of cos(bt).
Question 2
Easy
What shift do we apply for e^{-2t} f(t)?
💡 Hint: Remember the sign when applying the shift.
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 e^{2t} * sin(3t)?
- s^2 + 9
- (s-2)^2 + 9
- (s+2)^2 + 9
💡 Hint: Remember the shift rule defined by the theorem.
Question 2
True or False: The conditions s > Re(a) must be met when applying the First Shifting Theorem.
- True
- False
💡 Hint: Think about the nature of the exponentials involved.
Solve and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Using the First Shifting Theorem, compute the Laplace Transform of e^{-2t}cos(6t).
💡 Hint: What is the standard Laplace Transform for cos(bt)?
Question 2
Explain how the presence of e^{4t} affects the stability of the system modeled by the equation.
💡 Hint: Consider the implications of shifting the transform.
Challenge and get performance evaluation