Practice Special Case: Resonance (6.6) - Non-Homogeneous Equations

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6 sample questions

Question 1.
What is resonance?
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Think about when two frequencies blend together.
Question 2.
What adjustment should be made for the particular integral when resonance is present?
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Consider how resonance affects the functions involved.
3Question 3.
What is resonance?
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Consider scenarios where frequencies interact.
4Question 4.
True or False: The modification rule is not necessary when finding the particular integral in the case of resonance.
- True
- False
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Remember what happens when terms are too similar.
Question 5.
Given the differential equation $d^2y/dx^2 + 4y = \cos(2x)$ identify if resonance occurs, and if so, solve for y.
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Look for derivatives and matched frequencies.
Question 6.
Discuss how you would approach the design of a skyscraper to mitigate the effects of resonance during high winds.
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Consider balancing frequency to avoid synchronization.

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