2009501436_&igrave;œ&nbsp;&ecirc;&acute;‘&igrave;„&nbsp;_hw#2

# 2009501436_ìœ ê´‘ì„ _hw#2

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Home Work. #2 Problem Set 1.4 1.4.7) A difference of point loads, 1 2 ( ) ( ) ( ) 3 3 f x x x δ δ = - - + , does allow a free-free solution to '' u f - = . Find infinitely many solution with ' (0) 0 u = and ' (1) 0 u = . Sol) '' 1 2 ( ) ( ) ( ) 3 3 u f x x x δ δ - = = - - + x 3˜ ® ·ª* ( ) u x ® · 1 1 ( ) (0 ) 3 u x Ax B x = + 2 1 2 ( ) ( ) 3 3 u x Cx D x = + B.C : ' 1 (0) 0 u = , ' 3 (1) 0 u = 3 2 ( ) ( 1) 3 u x Ex F x = + B.Cx ® ' 1 (0) 0 0 u A = = g , ' 3 (1) 1 0 u E = = g 0 A = , 0 E = Drop by 1 in ' ( ) u x ' ' 1 2 ( ) ( ) 1 u x u x - = 1 A C - = , 1 C = And 1 2 , 3 3 x = 1 2 1 1 1 1 ( ) ( ) 0* -1* 3 3 3 3 u u B D = = + = + 1 3 D B = + 2 3 2 2 2 ( ) ( ) 1* 3 3 3 u u D F = = - + = 2 1 3 3 F D B = - = - Then, 1 1 ( ) (0 ) 3 u x B x = 2 1 1 2 ( ) ( ) 3 3 3 u x x B x = - + + 3 1 2 ( ) ( 1) 3 3 u x B x = - 2009-03-25 δ x 1 3 2 3 0 } B 1 3 B - 1 3 B + 2 3 1 3

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Home Work. #2 Problem Set 1.5 1.5.4) Verify that DST agrees with sin(JK*pi/6)/sqrt(3), and Test 1 T DST DST - = Sol) 5 2 -1 0 0 0 -1 2 -1 0 0 0 -1 2 -1 0 0 0 -1 2 -1 0 0 0 -1 2 K = , [ , ] ( ) Q E eig K = -0.2887 -0.5000 -0.5774 -0.5000 0.2887 -0.5000 -0.5000 0 0.5000 -0.5000 -0.5774 0.0000 -0.5774 0 0.5774 -0.5000 0.5000 0 -0.5000 -0.5000 -0.2887 0.5000 0.5774 0.5000 0.2887 Q = 0.2679 0 0 0 0 0 1.0000 0 0 0 0 0 2.0000 0 0 0 0 0 3.0000 0 0 0 0 0 3.7321 E
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