Use of diagonal matrices in vibration analysis?

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why are diagonal matrices and eigen vectors useful in vibrations analysis?
 

DrClaude

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Because the eigenvalues and eigenvectors correspond to normal modes.
 

fresh_42

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why are diagonal matrices and eigen vectors useful in vibrations analysis?
Because resonance is an eigenstate.
 

fresh_42

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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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