Use of diagonal matrices in vibration analysis?

AI Thread Summary
Diagonal matrices and eigenvectors are crucial in vibration analysis as they relate to normal modes and resonance, which are fundamental concepts in understanding system behavior. The eigenvalues indicate the natural frequencies of the system, while the eigenvectors represent the corresponding mode shapes. This relationship allows for simplified analysis of complex systems by reducing them to diagonal forms. The discussion also touches on the importance of engaging with both understood and unexplained concepts in physics education. Resources for further reading on these topics are sought after, highlighting the need for accessible educational materials.
theone
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why are diagonal matrices and eigen vectors useful in vibrations analysis?
 
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Because the eigenvalues and eigenvectors correspond to normal modes.
 
theone said:
why are diagonal matrices and eigen vectors useful in vibrations analysis?
Because resonance is an eigenstate.
 
DrClaude said:
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!
 
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