1.8.1 - Example 3
Enroll to start learning
You’ve not yet enrolled in this course. Please enroll for free to listen to audio lessons, classroom podcasts and take practice test.
Practice Questions
Test your understanding with targeted questions
Find the Laplace Transform of e^(2t) sin(t).
💡 Hint: Use the theorem to shift based on the coefficient of the exponent.
What do you change in the Laplace domain when you have e^(at)?
💡 Hint: Remember the theorem statement!
4 more questions available
Interactive Quizzes
Quick quizzes to reinforce your learning
What does the First Shifting Theorem allow you to do?
💡 Hint: Think about how exponential functions interact with transforms.
True or False: Multiplying a function by e^(3t) shifts to the right in the frequency domain.
💡 Hint: Recall the direction of the shift when applying the theorem.
1 more question available
Challenge Problems
Push your limits with advanced challenges
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).
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.
Get performance evaluation
Reference links
Supplementary resources to enhance your learning experience.