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(Solved): Find the natural frequencies of the below 3 DOF system. Show all working, and please ensure that the ...


Find the natural frequencies of the below 3 DOF system. Show all working, and please ensure that the answer matches the one provided.

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ANSWER:

\( 2.345 \sqrt{ }(\mathrm{k} / \mathrm{m}) ; 1.084 \sqrt{ }(\mathrm{k} / \mathrm{m}) ; 0.4575 \sqrt{ }(\mathrm{k} / \mathrm{m



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the natural frequencies of the below 3 DOF system



fundamental natural frequency of spring mass system using dunkerley's method
first influence coefficient for mass 2m are given as
?11=(1/3k); ?22=?33=(1/3k


second influence coefficients for mass 2m are given as
?22=((1/3k)+(1/2k))=((2+3)/(6k))
=(k/6k)
?21=(1/3k)




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