lec.30a.pptx folds (iii)

7/23/2019 Lec.30a.pptx Folds (III)

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d 2v

dx2 +

12Pv

BbH 3 = 0

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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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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"

# $

%

& '



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v = A1cos

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BbH 3

! " #

$ % & 1/2

x!

" #

$

% & + A2

sin 12P

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$ % & 1/2

x!

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$

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lec.30a.pptx folds (iii)

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