Practice Laplace Transform of the Dirac Delta Function - 10.2 | 10. The Dirac Delta Function (Impulse Function) | Mathematics - iii (Differential Calculus) - Vol 1
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Laplace Transform of the Dirac Delta Function

10.2 - Laplace Transform of the Dirac Delta Function

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Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is the value of the Dirac Delta function δ(t - a) when t = a?

💡 Hint: Think about the nature of the delta function.

Question 2 Easy

What does the Laplace transform of δ(t) equal?

💡 Hint: Consider the special case when a = 0 in the transform.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the Laplace transform of δ(t - 2)?

2e^{-2s}
e^{-2s}
1

💡 Hint: Use the standard formula of Laplace transform for δ(t - a).

Question 2

True or False: The area under the curve of the Dirac Delta function δ(t - a) is always equal to 1.

True
False

💡 Hint: Reflect on the properties of integrals involving the delta function.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

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.

Challenge 2 Hard

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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