Introducing Resonance Using computational thinking to teach mechanical vibrations
Introduction to Mechanical Vibrations is a 30+ year old upper level elective in the mechanical engineering curriculum at the University of California, Davis. It is a classic mechanical engineering course that stems from the courses and books of Timoshenko and Den Hartog from the early 20th century. The course advances students' understanding of vibrating mechanical systems, that has a foundation is the theory of small periodic motions resulting from the mathematical analysis of linear differential equations derived from Newton's Second Law of Motion. These foundational concepts provide insight into the design of machines to both minimize undesired vibrations and exploit desired vibrations.
Most mechanical vibration courses have been presented primarily from a theoretical perspective which was tied to the early analytic tools. There have also been some courses with accompanying laboratories to experiment with real vibrating systems, but those are fewer and far between. Also, since the late 80s, mechanical vibrations courses have often been enhanced with computational tools, such as Matlab, to solve problems that are difficult or unwieldy to solve by hand.
These courses typically have the standard engineering course format, i.e. the professor lectures in class by deriving mathematical theory on the board and does example problems to accompany the theory, the students are assigned homework problems each week for practice at applying and understanding the theory, and exams are given that are similar to homework problems to assess student learning.
This format has served the engineering profession well for a century or more, but there are a number of reasons to believe that this course could be changed to both improve learning and provide students with skills that are more relevant to their future work.