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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
State the definition of the unit step function.
💡 Hint: Think about what happens before and after time a.
Question 2
Easy
What is the Laplace Transform of u(t)?
💡 Hint: Recall how the unit step function behaves from a time perspective.
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 Laplace Transform of u(t-a)?
- 0
- 1
- e^{-as}/s
💡 Hint: Recall the definition of the transform.
Question 2
True or False: The unit step function can only take values 0 or 1.
- True
- False
💡 Hint: Think about the properties of the unit step function.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
For a function f(t) = sin(t) and a = 2, derive the Laplace Transform of f(t)u(t-2).
💡 Hint: Think about the second shifting theorem and how it applies here.
Question 2
Design a control system using u(t-1) that incorporates a delayed response. What does your Laplace Transform yield?
💡 Hint: Consider the implications of your delay in a real system.
Challenge and get performance evaluation