2 mass 3 spring system2 mass 3 spring example with "compatible" damping, treated first directly, then using reduction of order.
See the discussion of the webpages for the second order system in the 2-vector variable representing equal masses and spring constants:
http://www34.homepage.villanova.edu/robert.jantzen/courses/mat2705/handouts/redorder.pdf
http://www34.homepage.villanova.edu/robert.jantzen/courses/mat2705/handouts/redorderwithoutredexercise.pdf
followed by the request to use reduction of order to recover the same solution.
This system is more thoroughly examined from start to finish in:
http://www34.homepage.villanova.edu/robert.jantzen/courses/mat2705/handouts/2mass3spring.mw