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7/23/2019 Lec.30a.pptx Folds (III)
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7/23/2019 Lec.30a.pptx Folds (III)
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7/23/2019 Lec.30a.pptx Folds (III)
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7/23/2019 Lec.30a.pptx Folds (III)
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u y =!"
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7/23/2019 Lec.30a.pptx Folds (III)
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7/23/2019 Lec.30a.pptx Folds (III)
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7/23/2019 Lec.30a.pptx Folds (III)
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d 2v
dx2 +
12Pv
BbH 3 = 0
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c ^ :*<3d*4>2+ ,3->2479 `a94?>:b
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7/23/2019 Lec.30a.pptx Folds (III)
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d 2v
dx2 =
!12Pv
BbH 3
)*< -34=-*3,2+ .*< 7*-34=-*3,2+0 ;=47Q*4- >:9
-97*4, ,9<3J2QJ9 3- 6<*6*<Q*42+ >* >:9
49?2QJ9 *; >:9 *<3?342+ ;=47Q*4
Let v = A1cos
2! kx
L
" # $
% & '
dv
dx=
2! k
L
" # $
% & ' A
1sin
2! x
L
" # $
% & '
d 2v
dx2 =
2! k
L
" # $
% & ' 2! k
L
" # $
% & ' A
1 (cos
2! x
L
" # $
% & '
)
*+
,
-.
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/// B=7C+34? A97:2437-)*<A *; -*+=Q*4
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d 2v
dx2 =
!12Pv
BbH 3
v = A1 cos 2! kx
L
" # $
% & '
d 2v
dx2 =
2! k
L
" # $
% & '
2
A1 (cos 2! x
L
" # $
% & '
)
*+
,
-. =
(12Pv BbH
3 =
(12P BbH
3 A1 cos
2! x
L
" # $
% & '
)
*+
,
-.
Eliminating common terms
2! k
L" # $ % & '
2
= 12P
BbH 3 / 2
! k
L" # $ % & '
= 12P
BbH 3" # $ % & '
1/ 2
/ k = L
2! " # $ % & ' 12
P
BbH 3" # $ % & '
1/ 2
v = A1 cos 12P
BbH 3
" # $
% & ' 1/ 2
x"
# $
%
& '
7/23/2019 Lec.30a.pptx Folds (III)
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v = A1cos
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BbH 3
! " #
$ % & 1/2
x!
" #
$
% & + A2
sin 12P
BbH 3
! " #
$ % & 1/2
x!
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7/23/2019 Lec.30a.pptx Folds (III)
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