9.1.3 - Proof
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Practice Questions
Test your understanding with targeted questions
State the definition of the unit step function.
💡 Hint: Think about what happens before and after time a.
What is the Laplace Transform of u(t)?
💡 Hint: Recall how the unit step function behaves from a time perspective.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the Laplace Transform of u(t-a)?
💡 Hint: Recall the definition of the transform.
True or False: The unit step function can only take values 0 or 1.
💡 Hint: Think about the properties of the unit step function.
2 more questions available
Challenge Problems
Push your limits with advanced challenges
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.
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.
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