**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 .

Use the earthquake amplitude e =
0.075 ft = 0.9
in. for this example.

Solve the linear system using the parameters
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**.

Second, create the matrix .

Print the linear system we want to solve.

Third, solve the linear system using and e = 0.075.

We can convert these values to inches if desired.

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 ?

The maximum amplitude of oscillation in inches is:

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 ?

The minimum amplitude of oscillation in inches is:

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.

Now plot the functions.

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

(c) John H. Mathews 2004