Engineers and scientists use mass-spring models to gain insight into the dynamics of struc...

Engineers and scientists use mass-spring models to gain insight into the dynamics of structures under the influence of disturbances such as earthquakes. Figure P20.22 shows such a representation for a three-story building. For this case, the analysis is limited to horizontal motion of the structure. Using Newton’s second law, force balances can be developed for this system as

FIGURE P20.22

Simulate the dynamics of this structure from t = 0 to 20 s, given the initial condition that the velocity of the ground floor is dx1/dt = 1 m/s, and all other initial values of displacements and velocities are zero. Present your results as two time-series plots of (a) displacements and (b) velocities. In addition, develop a three-dimensional phase-plane plot of the displacements.