Model for Earthquake on a Tall Building

n

5

t

40.

m

10000.

k

11000.

γ

8000.

ω

1.

This is a rough model of the behavior of an idealized tall building undergoing horizontal seismic motion. The building has

n

floors supported by walls. (Each floor has mass

m

but the weight is not taken into account.) The displacements of the floors from their equilibrium positions are

x

1

,

x

2

, …,

x

n

; 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

k

. The diagonal lines represent shock absorbers that introduce a damping factor

γ

.