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{SECT 0 {PARA 256 "" 0 "" {TEXT -1 9 "Math 2250" }}{PARA 257 "" 0 "" 
{TEXT -1 34 "Earthquake project answer template" }}{PARA 258 "" 0 "" 
{TEXT -1 17 "November 20, 2000" }}{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 you
r 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 b
e using your student number to construct your building.  As the book i
nstructs on page 438, let the weight in tons of each story be given by
 the largest digit of your I.D. number, and let the spring constant k \+
(tons/foot) be the smallest digit of your I.D. number.  Deduce the mas
s of each floor (in slugs), and then define the mass and spring consta
nt values 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 f
or this system, the spring constant matrix K, and find the matrix \"A
\" as in equation (1),  page 437." }}{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)  Find the natural angular frequencies (the omegas) for your se
ven story building, as well as the corresponding periods.  Hint: MAKE \+
SURE THAT AT LEAST ONE ENTRY IN \"A\" IS IN DECIMAL (RATHER THAN FRACT
ION OR WHOLE NUMBER) FORM.  OTHERWISE MAPLE TRIES FINDING EIGENVALUES \+
AND EIGENVECTORS ALGEBRAICALLY INSTEAD OF NUMERICALLY, AND CAN FAIL." 
}}{PARA 0 "" 0 "" {TEXT -1 60 "Exhibit this data in a table like figur
e 7.4.17 on page 437." }}{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 study
ing the (undetermined coefficients) particular solution to (2), page 4
38, for your building.  The method is outlined on page 433 of the text
, and in the project notes which accompany this template.  Choose the \+
vector " }{TEXT 258 1 "b" }{TEXT -1 145 " appropriately in (2) so that
 it corresponds to a ground shaking amplitude of 3 inches (as suggeste
d by the warmup 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) solves (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 pic
ture like Figure 7.4.18, for your building.  Note that in this graph y
ou are to compute the norm of the " }{TEXT 259 1 "c" }{TEXT -1 58 "-ve
ctor as a function 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 y
our particular building susceptible to likely damage from an earthquak
e having its period in the 2 to 3 second range?  Explain." }}}{MARK "8
 0" 337 }{VIEWOPTS 1 1 0 1 1 1803 1 1 1 1 }{PAGENUMBERS 0 1 2 33 1 1 }