Example 2.  Solving the above non-homogeneous system for the coefficient vector  v  for  X[t].  
The vector  v  is the solution to the equation  [Graphics:Images/EarthQuakeModelMod_gr_45.gif].  
Use the earthquake amplitude  e = 0.075 ft = 0.9 in.  for this example.

Solve the linear system using the parameters  [Graphics:Images/EarthQuakeModelMod_gr_46.gif] and  e = 0.075.  

Find the coefficient vector  v  and the vector  X[t].  Plot the vibrations of each floor.

Solution 2.

First, enter the column vector  b.

[Graphics:../Images/EarthQuakeModelMod_gr_47.gif]

Second, create the matrix [Graphics:../Images/EarthQuakeModelMod_gr_48.gif].

[Graphics:../Images/EarthQuakeModelMod_gr_49.gif]



[Graphics:../Images/EarthQuakeModelMod_gr_50.gif]


Print the linear system we want to solve.

[Graphics:../Images/EarthQuakeModelMod_gr_51.gif]



[Graphics:../Images/EarthQuakeModelMod_gr_52.gif]


Third, solve the linear system using  [Graphics:../Images/EarthQuakeModelMod_gr_53.gif] and  e = 0.075.

[Graphics:../Images/EarthQuakeModelMod_gr_54.gif]



[Graphics:../Images/EarthQuakeModelMod_gr_55.gif]

[Graphics:../Images/EarthQuakeModelMod_gr_56.gif]


We can convert these values to inches if desired.

[Graphics:../Images/EarthQuakeModelMod_gr_57.gif]



[Graphics:../Images/EarthQuakeModelMod_gr_58.gif]

Fourth, find the maximum amplitude of oscillation of the floors in feet and in inches.
On what floor did the maximum amplitude of oscillation occur ?

 

[Graphics:../Images/EarthQuakeModelMod_gr_59.gif]

[Graphics:../Images/EarthQuakeModelMod_gr_60.gif]

The maximum amplitude of oscillation in inches is:

 

[Graphics:../Images/EarthQuakeModelMod_gr_61.gif]

[Graphics:../Images/EarthQuakeModelMod_gr_62.gif]

Notice that it occurs on the second floor.

Fifth, find the minimum amplitude of oscillation of the floors in feet and in inches.  
On what floor would did the minimum amplitude of of oscillation occur  ?

 

[Graphics:../Images/EarthQuakeModelMod_gr_63.gif]

[Graphics:../Images/EarthQuakeModelMod_gr_64.gif]

The minimum amplitude of oscillation in inches is:

 

[Graphics:../Images/EarthQuakeModelMod_gr_65.gif]

[Graphics:../Images/EarthQuakeModelMod_gr_66.gif]

Notice that it occurs on the fifth floor.

Sixth, form  X[t],  but plot  X[t] + k  for floor  k.  
Do this on one graph by forming a set of functions to plot parametrically.

[Graphics:../Images/EarthQuakeModelMod_gr_67.gif]



[Graphics:../Images/EarthQuakeModelMod_gr_68.gif]

[Graphics:../Images/EarthQuakeModelMod_gr_69.gif]


Now plot the functions.  
Imagine a vertical line through  x = 1,2,3,4,5,6  which would represent no movements of the floors.

[Graphics:../Images/EarthQuakeModelMod_gr_70.gif]


[Graphics:../Images/EarthQuakeModelMod_gr_71.gif]

[Graphics:../Images/EarthQuakeModelMod_gr_72.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004