Example 1.  Consider a building with  n = 6  floors each of mass  m = 1250 slugs (weight of 20 tons)
and the horizontal restoring force of   k = 10,000 lb/ft = 5 tons/foot  between floors.
Then  ,  and this system reduces to the form  

Compute the eigenvalues of matrix  ,
and the natural frequencies    and  periods  P  of oscillation of the building.

Solution 1.

Enter the matrix  a  into Mathematica.

Compute the eigenvalues of the matrix  a, and the natural frequencies    and  periods  p  of oscillation of the building.

		λ

(c) John H. Mathews 2004