One makes the assumption that the whole mass of the building is concentrating
in the ceilings. The steel framework of the building provides elastic
restoring forces proportional to the relative lateral displacement of the floors.
A damping force (proportional to the relative velocity of the floors) is added.
You will be given C-code to compile and run to study this problem. You should
get this program going (as discussed below) in your first session.
The equation of motion for any floor except for the ground floor and the top floor will then be :
where 
and 
are the displacement and velocity of the nth floor.
c is an elastic constant and b is a damping constant.
The equation of motion of the top floor is similar except the reactions from the floor above
are absent.
The ground floor is treated quite differently. We assume that the ground floor has horizontal
displacement of the form 
imposed on it by the earth.
We specify as inputs to the program what the values of A and 
are.
How do we organize the program to ensure that the horizontal displacement of the ground floor
is 
? By specifying in the derivatives routine (referred to as der above but
actually to be called multi below) that:
and:
