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program_4 - CE 335 Programming Assignment 4 Differential...

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CE 335 Programming Assignment 4 Differential Equations: Seismic response of buildings Horizontal acceleration of the ground during an earthquake causes shear stress on building members as the building tries to keep up with the ground motion. If the acceleration is too large, the building can fail and collapse. The response of the frames of multistory buildings to seismic forces can be roughly modeled as a system of differential equations describing coupled linear oscillators, one for each floor. For a building with n floors, this is a system of n second-order differential equations (which, as we learned, can be written as a system of 2 n first-order differential equations) in the n unknown displacements x ( t ) Mx' ' + Cx' + Kx = m a (1) where x is the n x 1 vector of the horizontal displacement of each floor, M is an n x n matrix with diagonal elements equal to the mass of each floor (and m is the corresponding n x 1 vector of the diagonal elements), C is an n x n
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