Practice Illustrative Examples (5.1.2.5) - Laplace Transform Analysis of Continuous-Time Systems
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Illustrative Examples

Practice - Illustrative Examples

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Practice Questions

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Question 1 Easy

What is the Laplace Transform of the unit step function?

💡 Hint: Recall the definition of the unit step function.

Question 2 Easy

What is the ROC for L{e^{-at}u(t)}?

💡 Hint: Consider the impact of the exponential decay.

4 more questions available

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Question 1

What is the Laplace Transform of the unit step function?

1/s
s
e^{-s}

💡 Hint: Think about what the unit step function signifies.

Question 2

True or False: The ROC for L{delta(t)} is the entire complex s-plane.

True
False

💡 Hint: Consider the nature of impulse functions and their transforms.

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Challenge Problems

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Challenge 1 Hard

Given a signal defined as x(t) = e^{-3t}u(t), find its Laplace Transform and explain its implications.

💡 Hint: Focus on applying the exponential transformation rule.

Challenge 2 Hard

For the function x(t) = sin(2t)u(t), determine the Laplace Transform and discuss the frequency aspects.

💡 Hint: Think about the sine function's periodic nature in relation to its transform.

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