Practice Core Concept (5.2.1.1) - Laplace Transform Analysis of Continuous-Time Systems
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Core Concept

Practice - Core Concept

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Practice Questions

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Question 1 Easy

What is the prerequisite condition for applying Partial Fraction Expansion?

💡 Hint: Think about what makes a rational function proper.

Question 2 Easy

Define a proper rational function.

💡 Hint: Check the degrees of numerator and denominator.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What technique is used for finding the inverse Laplace Transform of rational functions?

Direct Inversion
Partial Fraction Expansion
Polynomial Long Division

💡 Hint: Which method allows for decomposition into simpler parts?

Question 2

T/F: The degree of the numerator for an improper rational function is less than that of the denominator.

True
False

💡 Hint: Think of what defines a proper function in contrast to an improper one.

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Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the function 3s/(s^3 - 3s^2 + 3s - 3), perform a complete PFE and inverse transform.

💡 Hint: Evaluate at the poles after fraction decomposition for coefficient extraction.

Challenge 2 Hard

For a system described by the transfer function H(s), with both complex and repeated poles, determine the system's response based on the inverse Laplace Transform.

💡 Hint: Keep track of causality and ensure all conditions are met in your response.

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Reference links

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