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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the value of u(t-5) when t = 3?
💡 Hint: Think about the definition of the unit step function.
Question 2
Easy
Write the expression for the Laplace Transform of u(t-4).
💡 Hint: Consider the standard result we've just discussed.
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 unit step function u(t-a) equal for t < a?
- 0
- 1
- Undefined
💡 Hint: Recall the definition of the unit step function.
Question 2
The Laplace Transform of u(t-a) is which of the following?
- \\( \\frac{e^{-as}}{s} \\)
- \\( \\frac{a}{s} \\)
- s
💡 Hint: Consider the formula discussed in class.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Derive the Laplace Transform of the function f(t) = (3t + 2)u(t-1). What is the transformed function?
💡 Hint: Break it down, and remember to apply the theorem after recognizing the step function.
Question 2
Model a mechanical system experiencing a sudden force at t = 5 seconds. Write the governing differential equation and solve using Laplace Transform.
💡 Hint: Apply the Laplace Transform for each term, recalling initial conditions.
Challenge and get performance evaluation