6.6. Special Case: Resonance

Try these first

1. 1.

   What is resonance?

   Hint

   Think about when two frequencies blend together.

2. 2.

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

   Hint

   Consider how resonance affects the functions involved.

3. 3.

   What is resonance?

   Hint

   Consider scenarios where frequencies interact.

4. 4.

   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.

5. 5.

   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.

6. 6.

   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.