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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
Define the unit step function.
💡 Hint: Think about how the function behaves over time.
Question 2
Easy
What is the Laplace Transform of u(t−a)?
💡 Hint: Recall the formula we derived.
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 definition of the unit step function?
💡 Hint: Consider how the function activates.
Question 2
The Laplace Transform of u(t−a) is given by which formula?
- e^{−as}/s
- s/(e^{as})
- (1/s)e^{−as}
💡 Hint: Recall the transformation formula we discussed.
Solve 2 more questions and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Consider a switch that activates at t = 3 in a system described by the function f(t) = cos(t). Calculate the Laplace Transform of the system taking into account the unit step function.
💡 Hint: Use the property of shifting and recognize cos(t) transforms.
Question 2
A mechanical system experiences a sudden force at t = 4 described by the impulse m*d²x/dt² + kx = F(t)u(t−4). Derive the system response in the Laplace domain.
💡 Hint: Focus on the relationship established through the Laplace properties of derivatives.
Challenge and get performance evaluation