10.2 - Laplace Transform of the Dirac Delta Function
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Practice Questions
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What is the value of the Dirac Delta function δ(t - a) when t = a?
💡 Hint: Think about the nature of the delta function.
What does the Laplace transform of δ(t) equal?
💡 Hint: Consider the special case when a = 0 in the transform.
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Interactive Quizzes
Quick quizzes to reinforce your learning
What is the Laplace transform of δ(t - 2)?
💡 Hint: Use the standard formula of Laplace transform for δ(t - a).
True or False: The area under the curve of the Dirac Delta function δ(t - a) is always equal to 1.
💡 Hint: Reflect on the properties of integrals involving the delta function.
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Challenge Problems
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Given the function δ(t - 5), derive the system response when this impulse is applied to the system modeled by the equation dy/dt + 2y = δ(t - 5).
💡 Hint: Remember to handle the transform with impulse appropriately.
Illustrate how the impulse response can be utilized to design a control system, referencing δ(t) as an example.
💡 Hint: Think about how a system suite deals with feedback and transient states.
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