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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 11 "Math 2280-1" }}{PARA 257 "" 0 "
" {TEXT -1 34 "Earthquake project answer template" }}{PARA 258 "" 0 "
" {TEXT -1 17 "Due March 10 2006" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 192 "You may work in groups of up to three pe
ople.  Download this file from our lectures or homework page, or direc
tly open the URL http://www.math.utah.edu/~korevaar/2280spring06/quake
template.mws" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 
"" {MPLTEXT 1 0 49 "restart:\nwith(DEtools):with(plots):with(linalg):
\n" }}}{PARA 0 "" 0 "" {TEXT -1 49 "1)  Enter the names of the people \+
in your group! " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 450 "2)  You will be using yo
ur student number to construct your building.  As the book instructs o
n page 327, let the weight in tons of each story be given by the large
st digit of your I.D. number(s), and let the spring constant k (tons/f
oot) be the smallest digit in the  I.D. number of the person in your g
roup who has the largest digit!?  Deduce the mass of each floor (in sl
ugs), and then define the mass and spring constant values for your bui
lding." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{PARA 0 "" 0 "" {TEXT -1 208 "3)  Define the mass matrix M for thi
s system, the spring constant matrix K, and find the matrix \"A\" as i
n equation (1),  page 326.  Notice that the last row should look a lit
tle different than you may expect." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 341 "4)  Find the natural angular frequencies (the \+
omegas) for your seven story building, as well as the corresponding pe
riods.  Hint: MAKE SURE THAT AT LEAST ONE ENTRY IN \"A\" IS IN DECIMAL
 (RATHER THAN FRACTION OR WHOLE NUMBER) FORM.  OTHERWISE MAPLE TRIES F
INDING EIGENVALUES AND EIGENVECTORS ALGEBRAICALLY INSTEAD OF NUMERICAL
LY, AND CAN FAIL." }}{PARA 0 "" 0 "" {TEXT -1 227 "Exhibit this data i
n a table like figure 5.3.17 on page 327.  (I would make the table in \+
a text field and copy and paste the Maple output into the text table. \+
 But leave in the Maple commands which give you the various values!)" 
}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 245 "5)  Study approximate resonance by study
ing the (undetermined coefficients) particular solution to (2), page 3
27, for your building.  The method is outlined on page 323 of the text
, and in the class notes from Monday March 6.  Choose the vector " }
{TEXT 258 1 "b" }{TEXT -1 145 " appropriately in (2) so that it corres
ponds to a ground shaking amplitude of 3 inches (as suggested by the w
armup problem #4).  Find the vector " }{TEXT 256 1 "c" }{TEXT -1 27 " \+
(depending on w)  so that " }{TEXT 257 1 "c" }{TEXT -1 20 "*cos(wt) so
lves (2):" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 
0 "" }}{PARA 0 "" 0 "" {TEXT -1 143 "6)  Create an approximate resonan
ce picture like Figure 5.3.18, for your building.  Note that in this g
raph you are to compute the norm of the " }{TEXT 259 1 "c" }{TEXT -1 
58 "-vector as a function of period, not of angular frequency." }}
{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 
0 "" 0 "" {TEXT -1 135 "7)  Is your particular building susceptible to
 likely damage from an earthquake having its period in the 2 to 3 seco
nd range?  Explain." }}}{MARK "26 0" 0 }{VIEWOPTS 1 1 0 1 1 1803 1 1 
1 1 }{PAGENUMBERS 0 1 2 33 1 1 }