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Normal modes of two equal masses between three springs
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Physics
Branch of physics
Classical mechanics
Lagrangian mechanics
Small oscillation
Generalized eigenvalue problem for small oscillations
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Words: 40
For equal masses
m
, wall-spring constants
k
1
,
k
2
, and coupling-spring constant
k
3
, the
small-oscillation mass and stiffness matrices
are
M
=
m
I
,
K
=
(
k
1
+
k
3
−
k
3
−
k
3
k
2
+
k
3
)
.
(49)
If
k
1
=
k
(
1
+
ε
δ
)
,
k
2
=
k
(
1
−
ε
δ
)
, and
k
3
=
k
ε
, the squared normal frequencies are
ω
±
2
=
m
k
[
1
+
ε
(
1
±
1
+
δ
2
)
]
.
(50)
Ancestors
(7)
Generalized eigenvalue problem for small oscillations
Small oscillation
Lagrangian mechanics
Classical mechanics
Branch of physics
Physics
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