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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 9 "Math 2280" }}{PARA 257 "" 0 "" 
{TEXT -1 34 "Earthquake project answer template" }}{PARA 258 "" 0 "" 
{TEXT -1 10 "March 2001" }}{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 41 "1)  Enter your name \+
and student number.  " }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 
"" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 392 "2)  You will be using
 your student number to construct your building.  As the book instruct
s on page 334, let the weight in tons of each story be given by the la
rgest digit of your I.D. number, and let the spring constant k (tons/f
oot) be the smallest digit of your I.D. number.  Deduce the mass of ea
ch floor (in slugs), and then define the mass and spring constant valu
es for your building." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 
0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}
{PARA 0 "" 0 "" {TEXT -1 130 "3)  Define the mass matrix M for this sy
stem, the spring constant matrix K, and find the matrix \"A\" as in eq
uation (1),  page 333." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG 
{PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }
}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 341 "4)  Fin
d the natural angular frequencies (the omegas) for your seven story bu
ilding, as well as the corresponding periods.  Hint: MAKE SURE THAT AT
 LEAST ONE ENTRY IN \"A\" IS IN DECIMAL (RATHER THAN FRACTION OR WHOLE
 NUMBER) FORM.  OTHERWISE MAPLE TRIES FINDING EIGENVALUES AND EIGENVEC
TORS ALGEBRAICALLY INSTEAD OF NUMERICALLY, AND CAN FAIL." }}{PARA 0 "
" 0 "" {TEXT -1 60 "Exhibit this data in a table like figure 5.3.17 on
 page 333." }}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{EXCHG {PARA 0 "> " 0 "
" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "
" {TEXT -1 257 "5)  Study approximate resonance by studying the (undet
ermined coefficients) particular solution to (2), page 334, for your b
uilding.  The method is outlined on page 329 of the text, and in the p
roject notes which accompany this template.  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 "" }}{EXCHG {PARA 0 "> " 0 "" 
{MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" {TEXT -1 0 "" }}{PARA 0 "" 0 "" 
{TEXT -1 143 "6)  Create an approximate resonance picture like Figure \+
5.3.18, for your building.  Note that in this graph you are to compute
 the norm of the " }{TEXT 259 1 "c" }{TEXT -1 58 "-vector as a functio
n of period, not of angular frequency." }}{PARA 0 "" 0 "" {TEXT -1 0 "
" }}{EXCHG {PARA 0 "> " 0 "" {MPLTEXT 1 0 0 "" }}}{PARA 0 "" 0 "" 
{TEXT -1 0 "" }}{PARA 0 "" 0 "" {TEXT -1 135 "7)  Is your particular b
uilding susceptible to likely damage from an earthquake having its per
iod in the 2 to 3 second range?  Explain." }}}{MARK "26 0" 59 }
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