(Solved): Periods of a 3-DOF system are \( 0.8 \mathrm{sec}, 0.35 \mathrm{sec} \), and \( 0.15 \mathrm{sec} \ ...

Periods of a 3-DOF system are \( 0.8 \mathrm{sec}, 0.35 \mathrm{sec} \), and \( 0.15 \mathrm{sec} \). The damping ratio is identified as \( 5 \% \) for all the modes from a forced vibration test. (a) A Rayleigh damping matrix is constructed such that the damping ratio is \( 5 \% \) for the first and third modes. Compute the damping ratio for the second mode. What is the error of computed damping ratio with respect to the identified? (b) What would the computed damping ratio in the second mode be if Caughey damping or Modal damping were used? Note: Refer to Lecture9 MDOF Damping slides