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Model for Earthquake on a Tall Building

This is a rough model of the behavior of an idealized tall building undergoing horizontal seismic motion. The building has floors supported by walls. (Each floor has mass but the weight is not taken into account.) The displacements of the floors from their equilibrium positions are , , …, ; initially these displacements and their velocities are set to zero. Each floor experiences a restoring forces from its contiguous floors according to Hooke's law with a spring constant . The diagonal lines represent shock absorbers that introduce a damping factor .

DETAILS

The equation of motion for the floor is
.
The equation for the first floor is
,
where is the function that represents the motion of the ground, which in this case is of the form .
For the floor,
.
Reference
[1] J. R. Brannan and W. E. Boyce, Differential Equations: An Introduction to Modern Methods and Applications, 2nd ed., New York: John Wiley & Sons, 2011 pp. 466–468.

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