Practice Case 2: Repeated Real Poles (5.2.1.3.2) - Laplace Transform Analysis of Continuous-Time Systems
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Case 2: Repeated Real Poles

Practice - Case 2: Repeated Real Poles

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Practice Questions

Test your understanding with targeted questions

Question 1 Easy

Define what a repeated pole is in the context of Laplace Transforms.

💡 Hint: Think about the multiplicity of roots.

Question 2 Easy

What is the cover-up method?

💡 Hint: It's a quick way to find coefficients.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is the form of the PFE for repeated real poles?

A. \\frac{A_1}{(s - p_1)} + \\frac{A_2}{(s - p_1)^2}
B. \\frac{A_1}{(s - p_1)} + \\frac{A_2}{(s - p_1)^2} + \\cdots + \\frac{A_n}{(s - p_1)^n}
C. All of the above

💡 Hint: Think about how we define the terms for all n.

Question 2

True or False: The cover-up method can only be used for terms not at the highest power of the pole.

True
False

💡 Hint: Remember the applications of the cover-up method.

1 more question available

Challenge Problems

Push your limits with advanced challenges

Challenge 1 Hard

Given the function X(s) = \frac{4}{(s - 5)^4}, perform a complete partial fraction expansion and list all coefficients.

💡 Hint: Use the coefficients for each power carefully.

Challenge 2 Hard

Discuss the stability implications of a system that has repeated poles in the right-half plane.

💡 Hint: Connect pole position to system response characteristics.

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