Reading:
- Lessons 28D, 29A, and 29B (pages 338-365)
Homework:
- The following exercises from Lesson 28D (p343):
- 3, 5, 8, 13
- For 5, the MOUC does not quite apply the way we learned it. The full version of the MOUC does apply, but you have to use the linearly independent derivatives of
instead of 
when coming up with your guess (remember what happened on exercise 21.22 of assignment 6?). Variation of parameters would work with no issues. Also, the solution is given in (28.93) on p340. - For 13, note that the textbook uses the term "frequency" for both angular frequency and actual frequency. It looks like they are referring to angular frequency in this exercise.
- The following exercises from Lesson 29A (p353):
- The following exercises from Lesson 29B (p364):
- 8, 9
- For 8, f(t) is assumed to be sinusoidal, just like in equation (29.41) on p360. The text should have explicitly made that assumption.
- You can ignore 9b, it's just some extra terminology. It's coming from a way of thinking about the damped oscillator setup as a "device" (much like a 4B student) into which one "inputs" a forcing function and the device "outputs" for you the response of the system, i.e. the solution of the ODE.
Videos:
vibrating table
Each of the three objects on the table has some resonant frequency, a frequency that, when used in a forcing function, maximizes the amplitude of the outcome. You can calculate the resonant frequency yourself given the damping coefficient and the natural frequency of oscillation. It's computed in the book in (29.53) on p361. It's just the value of the forcing frequency that maximizes the amplitude of the particular solution (which you can get using the MOUC, for example). You can see how, at different points in the video, the frequency of the table's vibration hits the resonant frequencies of the different objects.
Also: bridge video