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14
The homogeneous equations (Equations 11.4.10) for the two components of the j
th
eigenvector are …
22
1
12
2
0
j
j
a
lg
l
a
ll
g
ωω
−+
−
=
−−
+
Inserting the larger eigenfrequency (the (+) solution for
2
ω
above) into the upper
homogeneous equation yields the solution for the components of the 1
st
eigenvector …
()
1
1
11
2
1
21
a
l
a
−+ −
=
0
2
1
2 12
1
11
21
21
l l
ga
ga
++
+
+
−=
2
1 2
21
11
2
ll l l
aa
l
+
=
for the higher frequency, antisymmetric mode.
Inserting the smaller eigenfrequency (the () solution for
2
) into the upper
homogeneous equation yields the solution for the components of the 2
nd
eigenvector …
1
2
12
2
2
22
a
l
a
=
0
22
12
2
l
+
=
for the lower frequency, symmetric mode.
Again, we let a
11
= 1 and
a
21
= 1, since only ratios of the components of a given eigen
vector can be determined.
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This note was uploaded on 01/06/2012 for the course PHYSICS 4360C taught by Professor Johnanderson during the Fall '11 term at UNF.
 Fall '11
 JohnAnderson
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