Many of the applications from Section 1.8 can be solved using this method. Exercise 2 emphasizes that the Extended Linearity Principle for nonhomogeneous equations is different from the Linearity Principle for homogeneous equations. The approach is again fairly standard except for the fact that complex exponentials are used in the guess and test step of the Method of Undetermined Coefficients. This simplifies the guessing procedure and reinforces the use of complex numbers begun in Chapter 3. It also works well with the notion of phasors which are standard in Electric Circuit Theory.
Resonance is introduced by example and the qualitative analysis is done from the formulas.
Exercise 7 touches on the notions of natural response and forced response. These are covered in more detail in Section 5.3. Exercises 8 and 9 are essay problems on resonance. We believe the story in Exercise 9 is true, but can't remember the name of the University. If you happen to know more about this story, we would love to hear about it.