why are diagonal matrices and eigen vectors useful in vibrations analysis?
Because the eigenvalues and eigenvectors correspond to normal modes.
Because resonance is an eigenstate.
Be careful about that example: https://www.physicsforums.com/threads/expunging-myths-from-the-classrooom.849853
Thank you! And 'classroom' was exactly where I got it from ...
EDIT: “My experience is that excitement and interest in physics and engineering is generated not only by what is understood but also by what is not.” - Bernard Feldman, a physics professor at the University of Missouri, wrote in 2006.
A wise man!
do you know a website/textbook that explains the exact content in those slides in more detail?
Separate names with a comma.