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

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

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DrClaude

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Because the eigenvalues and eigenvectors correspond to normal modes.

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fresh_42

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

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DrClaude

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Be careful about that example: https://www.physicsforums.com/threads/expunging-myths-from-the-classrooom.849853Because resonance is an eigenstate.

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fresh_42

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Thank you! And 'classroom' was exactly where I got it from ...Be careful about that example: https://www.physicsforums.com/threads/expunging-myths-from-the-classrooom.849853

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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http://academic.csuohio.edu/richter_h/courses/mce371/mce371_14.pdfBecause the eigenvalues and eigenvectors correspond to normal modes.

do you know a website/textbook that explains the exact content in those slides in more detail?

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