Practice Step 4: Partial Fraction Expansion (pfe) (5.4.1.3.4) - Laplace Transform Analysis of Continuous-Time Systems
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Step 4: Partial Fraction Expansion (PFE)

Practice - Step 4: Partial Fraction Expansion (PFE)

Learning

Practice Questions

Test your understanding with targeted questions

Question 1 Easy

What is meant by a proper rational function?

💡 Hint: Check the degrees of both polynomials.

Question 2 Easy

What must be included when decomposing complex conjugate poles?

💡 Hint: Consider the form of the quadratic expression.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What condition must a rational function meet to apply Partial Fraction Expansion directly?

The degree of the numerator is less than that of the denominator
The numerator must be equal to the denominator
The denominator must have only positive roots

💡 Hint: Think about how degrees of polynomials work.

Question 2

True or False: The cover-up method can be used to find coefficients for repeated poles.

True
False

💡 Hint: Recall the methods for distinct versus repeated poles.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Consider X(s) = (s^3 + 5s) / ((s+1)(s^2 + 2s + 5)). Apply PFE to this function and specify the steps needed.

💡 Hint: Use polynomial long division if needed.

Challenge 2 Hard

Given X(s) = 1 / (s^3 + 2s^2 + s) apply PFE and describe how you would handle the multiple roots present.

💡 Hint: Start with polynomial factorization.

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Reference links

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