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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^(2t) sin(t).
💡 Hint: Use the theorem to shift based on the coefficient of the exponent.
Question 2
Easy
What do you change in the Laplace domain when you have e^(at)?
💡 Hint: Remember the theorem statement!
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 does the First Shifting Theorem allow you to do?
- Transform functions without any shifts
- Shift the s variable based on an exponential term
- Only apply to periodic functions
💡 Hint: Think about how exponential functions interact with transforms.
Question 2
True or False: Multiplying a function by e^(3t) shifts to the right in the frequency domain.
- True
- False
💡 Hint: Recall the direction of the shift when applying the theorem.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Demonstrate the application of the First Shifting Theorem in solving a second-order differential equation involving e^(3t) sin(2t). Provide the full steps.
💡 Hint: Start with the standard transform of sin(2t).
Question 2
Find the Laplace Transform of e^(-4t) (t² + t) and interpret the results given how the theorem modifies it.
💡 Hint: Ensure you manage each component separately and apply the shift afterwards.
Challenge and get performance evaluation