The given figure shows a model for a three-story building. Add a fourth floor with a mass of m4=6000kg connected with the third floor by a spring with k4=1200kN/m. Each floor mass is represented by mk, and each floor stiffness is represented by k for i=1 to 4 . 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 the system as follows: (m1k1+k2n2)X1m1k2X2=0m2k3X1+(m2k2+k3n2)X2m2k2X3=0m1k3X2+(mmk3+k4n2)X3m 1k4X4=0m4k4X3+(m4k4n2)X4=0 where Xj represent horizontal floor translations (m), and n is the natural, or resonant, frequency (radians/s). The resonant frequency can be expressed in Hertz (cycles/s) by dividing it by 2 radians/cycle. Sraphically represent the modes of vibration for the structure by displaying the amplitudes versus height for each of the eigenvectors..

1. The given figure shows a model for a three-story building. Add a fourth floor with a mass of
m4=6000kg connected with the third floor by a spring with k4=1200kN/m. Each floor mass is
represented by mk, and each floor stiffness is represented by k for i=1 to 4 . 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 the system as
follows:
(m1k1+k2n2)X1m1k2X2=0m2k3X1+(m2k2+k3n2)X2m2k2X3=0m1k3X2+(mmk3+k4n2)X3m
1k4X4=0m4k4X3+(m4k4n2)X4=0 where Xj represent horizontal floor translations (m), and n is
the natural, or resonant, frequency (radians/s). The resonant frequency can be expressed in Hertz
(cycles/s) by dividing it by 2 radians/cycle. Sraphically represent the modes of vibration for the
structure by displaying the amplitudes versus height for each of the eigenvectors.