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Practice Questions
Test your understanding with targeted questions related to the topic.
Question 1
Easy
What is the value of the Dirac Delta function Ξ΄(t - a) when t = a?
π‘ Hint: Think about the nature of the delta function.
Question 2
Easy
What does the Laplace transform of Ξ΄(t) equal?
π‘ Hint: Consider the special case when a = 0 in the transform.
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 Ξ΄(t - 2)?
- 2e^{-2s}
- e^{-2s}
- 1
π‘ Hint: Use the standard formula of Laplace transform for Ξ΄(t - a).
Question 2
True or False: The area under the curve of the Dirac Delta function Ξ΄(t - a) is always equal to 1.
- True
- False
π‘ Hint: Reflect on the properties of integrals involving the delta function.
Solve 1 more question and get performance evaluation
Challenge Problems
Push your limits with challenges.
Question 1
Given the function Ξ΄(t - 5), derive the system response when this impulse is applied to the system modeled by the equation dy/dt + 2y = Ξ΄(t - 5).
π‘ Hint: Remember to handle the transform with impulse appropriately.
Question 2
Illustrate how the impulse response can be utilized to design a control system, referencing Ξ΄(t) as an example.
π‘ Hint: Think about how a system suite deals with feedback and transient states.
Challenge and get performance evaluation