The given figure shows a model for a two-story building. Each floor mass is represented bym pand each floor stiffness is represented byk iâfori=1to 2 . For this case, the analysis is limited to horizontal motion of the structure as it is subjected to horizontal base motion due to earthquakes. The dynamic force balances can be developed for this system as follows.( m 1âk 1â+k 2ââÏ 2)X 1ââ m 1âk 2ââX 2â=0â m 2âk 2ââX 1â+( m 2âk 2âââÏ 2)X 2â=0âwhereX iârepresent horizontal floor translations(m), andÏ nâis the natural, or resonant, frequency (radians/s). The resonant frequency can be expressed in Hertz (cycles/s) by dividing it by2Ïradians/cycle. Use MATLAB to determine the eigenvalues, elgenvectors, and frequencies for the given system. (Round the final answers to four decimal places. Include a minus sign if necessary.) The eigenvalues=[ d 1â0â0d 2ââ]The value ofα 1â=The value ofd 2â=The eigenvectors=[ 0.8232eâdfâ]The value ofd=The value ofe=The value off=The frequencies of the two modes aref 1â=Hzandf 2â=1
