Determine the natural frequencies - shear building, Civil Engineering

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For the shear building shown, determine the natural frequencies (RAD/SEC) and the modal matrix. Also, sketch the deflected buildings in their normal modes using the top floor as the reference floor (set its displacement = unity). Finally, demonstrate orthogonality between the modes with example calculation. Each k factor (stiffness) = 15,000 LB/IN (that is, k1=k2=k3=k4=15,000 LB/IN)

m₁ = 50 LB-SEC²/IN

m₂ = 150 LB-SEC²/IN

Rigid crossbars

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