Practice Special Case: Resonance - 6.6 | 6. Non-Homogeneous Equations | Mathematics (Civil Engineering -1)
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Special Case: Resonance

6.6 - Special Case: Resonance

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Practice Questions

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Question 1 Easy

What is resonance?

💡 Hint: Think about when two frequencies blend together.

Question 2 Easy

What adjustment should be made for the particular integral when resonance is present?

💡 Hint: Consider how resonance affects the functions involved.

4 more questions available

Interactive Quizzes

Quick quizzes to reinforce your learning

Question 1

What is resonance?

💡 Hint: Consider scenarios where frequencies interact.

Question 2

True or False: The modification rule is not necessary when finding the particular integral in the case of resonance.

True
False

💡 Hint: Remember what happens when terms are too similar.

1 more question available

Challenge Problems

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Challenge 1 Hard

Given the differential equation \(d^2y/dx^2 + 4y = \cos(2x)\) identify if resonance occurs, and if so, solve for y.

💡 Hint: Look for derivatives and matched frequencies.

Challenge 2 Hard

Discuss how you would approach the design of a skyscraper to mitigate the effects of resonance during high winds.

💡 Hint: Consider balancing frequency to avoid synchronization.

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