Professional Courses
Industry-relevant training in Business, Technology, and Design to help professionals and graduates upskill for real-world careers.
Categories
Interactive Games
Fun, engaging games to boost memory, math fluency, typing speed, and English skills—perfect for learners of all ages.
Typing
Memory
Math
English Adventures
Knowledge
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