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some question in eigenfrequency .

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Hi
I used solid mechanics modeI and I have some confusions about the eigen frequency,so can you give some sugggestions?Any reply I will be very grateful.
Questions:
1、I just used solid mechanics mode to calculated the eigenfrequency,I find that eigenfrequency have the real part and the imaginary part when i add damp to the mode,so what do the two part means?
2、I got some results,when i didn't add damp,the eigenfrequency is 7.7317 ,and the result changed to 7.7909+0.95911i when i added damp .So can you explain the differences? By the way,i find 7.7317^2 is equal to 7.7909^2-0.95911^2,so it is a coincidence or inevitable result?

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