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

ISBN: 9780073401102 336

## Solution for problem 22.22 Chapter 22

Applied Numerical Methods W/MATLAB: for Engineers & Scientists | 3rd Edition

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Problem 22.22

Engineers and scientists use mass-spring models to gain insight into the dynamics of structures under the influence of disturbances such as earthquakes. Figure P22.22 shows such a representation for a three-story building. For this case, the analysis is limited to horizontal motion of the structure. Using Newtons second law, force balances can be developed for this system as d2x1 dt2 = k1 m1 x1 + k2 m1 (x2 x1) d2x2 dt2 = k2 m2 (x1 x2) + k3 m2 (x3 x2) d2x3 dt2 = k3 m3 (x2 x3) 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.

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