Lesson 6: Non-Homogeneous SOLDEs
Preview
Ensuring a smooth car ride isn't the only thing a damping mechanism is good for. Another, much more important application is to earthquake-proofing buildings. In this lesson we'll develop a simplified model of the displacement of a building during an earthquake. As we'll see, the resulting model will be a non-homogeneous SOLDE. We'll spend the rest of the lesson developing the necessary theory and techniques to solve such SOLDEs. We'll then return in the practice problems to the earthquake-proofing application and extract a few mathematical pointers for earthquake-proofing buildings.
We'll begin in Module I by setting up the investigation and the model for a building's sway during a hypothetical earthquake.
In Module II we'll build up the necessary theory needed to solve non-homogeneous SOLDEs and also discuss one simple technique for doing so.
We'll finish the lesson in Module III with a discussion of a more advanced technique for solving non-homogeneous SOLDEs.
Review
Learn
Work through the lesson notes below, consulting the videos below it when you get to the "See Class Notes" boxes. For your records, the annotated lesson notes are below the videos. Some tips for you as you work through these resources:
I recommend using Cornell Notes (or a modification of it; see this video starting at the 1:05 mark) to take notes on the lesson and the videos. This note-taking method balances detail with big-picture thinking to help you summarize and retain what you are learning. See this other video for additional note-taking techniques you might want to experiment with.
Lesson Notes
Lesson 6.pdfClass Notes A
Class Notes B
Class Notes C
Reflect
If you are currently enrolled in this course with me, submit the written reflections Google Form I have emailed you after working through the lesson notes and videos. Some tips:
Submit substantive, but concise, answers to each question; you will be doing the future you a big favor by taking time now to accurately and succinctly summarize what you have learned from the lesson.
Send yourself a copy of your reflections; they will come in handy later when you start preparing for quizzes and other assessments.
If you are not currently enrolled in this course with me, those written reflections ask three reflective questions designed to help you retain what you've learned and pinpoint any remaining areas of confusion. Those questions are:
Please summarize the main mathematical takeaways from the lesson notes.
What was the most interesting part of what you learned, and why?
What, if anything, do you still find confusing?
Practice
Work through the practice problems suggested below to see how much of this lesson you've understood.
Lesson 6 - Practice Problems.pdf