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 definition of the unit step function?
💡 Hint: Think about how it models sudden changes.
Question 2
Easy
What is the Laplace Transform of \( u(t) \)?
💡 Hint: Remember it's the transform of the basic unit step function.
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 \( u(t-a) \)?
- \\( \\frac{1}{s} \\)
- \\( \\frac{e^{-as}}{s} \\)
- \\( s \\)
💡 Hint: Focus on how the step function impacts transformation.
Question 2
True or False: The unit step function is always equal to 1.
- True
- False
💡 Hint: Recall the conditions for the unit step function.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a mechanical system where a force is applied at t=2 seconds. Model the system using the unit step function and derive the Laplace Transform of the applied force.
💡 Hint: Think about the timing and impact of the function before and after the shift.
Question 2
For the piecewise function defined as \( f(t) = t \cdot u(t-1) + 2 \cdot u(t-2) \), calculate its Laplace Transform.
💡 Hint: Separate each part according to the shifting theorem.
Challenge and get performance evaluation