wzory_dynamika.pdf

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Wzory transformacyjne drgań harmonicznych
F i
i
k
2
l mw
F k
l=
4
l
EJ
w
W i
W k
EJ
w
F
=
[
a
'
'
(
l
)
j
+
J
'
'
(
l
)
i
]
i
i
l
l
EJ
w
W
=
[
J
'
'
(
l
)
j
+
g
'
'
(
l
)
i
]
i
i
EJ
w
w
2
l
l
F
=
[
a
(
l
)
j
+
b
(
l
)
j
+
J
(
l
)
i
-
d
(
l
)
k
]
i
i
k
l
l
l
EJ
w
w
F
=
[
b
(
l
)
j
+
a
(
l
)
j
+
d
(
l
)
i
-
J
(
l
)
k
]
k
i
k
l
l
l
EJ
w
w
W
=
[
J
(
l
)
j
+
d
(
l
)
j
+
g
(
l
)
i
-
e
(
l
)
k
]
EJ
w
i
i
k
2
l
l
l
F
=
[
a
'
'
(
l
)
j
-
J
'
'
(
l
)
k
]
k
k
l
l
EJ
w
w
W
=
-
[
d
(
l
)
j
+
J
(
l
)
j
+
e
(
l
)
-
g
(
l
)
]
i
k
EJ
w
k
i
k
2
l
l
l
W
=
-
[
J
'
'
(
l
)
j
-
g
'
'
(
l
)
k
]
k
k
2
l
l
EJ
w
w
F
=
[
a
'
(
l
)
j
+
J
'
(
l
)
i
-
d
'
(
l
)
k
]
i
i
l
l
l
EJ
w
w
EJ
w
w
W
=
[
g
'
'
'
(
l
)
i
-
e
'
'
'
(
l
)
k
]
W
=
[
J
'
(
l
)
j
+
g
'
(
l
)
i
-
e
'
(
l
)
k
]
i
2
l
l
l
i
i
2
l
l
l
EJ
w
w
EJ
w
w
W
=
-
[
e
'
'
'
(
l
)
i
-
g
'
'
'
(
l
)
k
]
k
W
=
-
[
d
'
(
l
)
j
+
e
'
(
l
)
i
-
c
'
(
l
)
k
]
2
l
l
l
k
i
2
l
l
l
2
b
(
l
)
2
sh
l
sin
l
a
'
(
l
)
=
a
(
l
)
-
=
l
a
(
l
)
ch
l
sin
l
-
sh
l
cos
l
b
(
l
)
d
(
l
)
ch
l
sin
l
+
sh
l
cos
l
EJ
w
w
2
J
'
(
l
)
=
J
(
l
)
-
=
l
F
=
[
a
'
(
l
)
j
+
d
'
(
l
)
i
-
J
'
(
l
)
k
]
a
(
l
)
ch
l
sin
l
-
sh
l
cos
l
k
k
l
l
l
b
(
l
)
J
(
l
)
sh
l
+
sin
l
EJ
w
w
2
d
'
(
l
)
=
d
(
l
)
-
=
l
W
=
[
d
'
(
l
)
j
+
c
'
(
l
)
i
-
e
'
(
l
)
k
]
a
(
l
)
ch
l
sin
l
-
sh
l
cos
l
i
k
2
l
l
l
d
2
(
l
)
2
ch
l
cos
l
EJ
w
w
3
g
'
(
l
)
=
g
(
l
)
-
=
l
W
=
-
[
J
'
(
l
)
j
+
e
'
(
l
)
-
g
'
(
l
)
]
i
k
a
(
l
)
ch
l
sin
l
-
sh
l
cos
l
k
k
2
l
l
l
d
(
l
)
J
(
l
)
ch
l
+
cos
l
e
'
(
l
)
=
e
(
l
)
-
=
l
3
a
(
l
)
ch
l
sin
l
-
sh
l
cos
l
2
J
(
l
)
1
+
ch
l
cos
l
ch
l
sin
l
-
sh
l
cos
l
3
c
'
(
l
)
=
g
(
l
)
-
=
l
a
(
l
)
=
l
a
(
l
)
ch
l
sin
l
-
sh
l
cos
l
1
-
ch
l
cos
l
sh
l
-
sin
l
2
d
'
(
l
)
ch
l
sin
l
-
sh
l
cos
l
b
(
l
)
=
l
a
'
'
(
l
)
=
a
'
(
l
)
-
=
-
l
1
-
ch
l
cos
l
c
'
(
l
)
1
+
ch
l
cos
l
sh
l
sin
l
d
'
(
l
)
e
'
(
l
)
sh
l
sin
l
2
J
(
l
)
=
l
2
J
'
'
(
l
)
=
J
'
(
l
)
-
=
-
l
1
-
ch
l
cos
l
c
'
(
l
)
1
+
ch
l
cos
l
ch
l
-
cos
l
2
e
'
(
l
)
ch
l
sin
l
+
sh
l
cos
l
d
(
l
)
=
l
2
g
'
'
(
l
)
=
g
'
(
l
)
-
=
-
l
3
1
-
ch
l
cos
l
c
'
(
l
)
1
+
ch
l
cos
l
ch
l
sin
l
+
sh
l
cos
l
3
g
(
l
)
=
l
2
3
J
'
(
l
)
l
ch
l
sin
l
-
sh
l
cos
l
1
-
ch
l
cos
l
g
'
'
'
(
l
)
=
g
'
(
l
)
-
=
-
a
'
(
l
)
2
sh
l
sin
l
sh
l
+
sin
l
3
e
(
l
)
=
l
J
'
(
l
)
d
'
(
l
)
l
3
sh
l
-
sin
l
1
-
ch
l
cos
l
e
'
'
'
(
l
)
=
e
'
(
l
)
-
=
a
'
(
l
)
2
sh
l
sin
l
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