homework 10 solutions - Engineering Math Homework 10...

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Engineering Math Homework 10 Solutions Spring 2009 `? `> `B ## œ"' ?Ð!ß >Ñ œ ! ?Ð ß >Ñ œ ! >  ! and for 1 # ?ÐBß !Ñ œ 0ÐBÑ œ 'B ? ÐBß !Ñ œ 1ÐBÑ œ B !  B  sin cos and for > 1 # -œ% 1 # form of solution: ?ÐBß >Ñ œ F )8>  F )8> #8B ! ’“ 8œ" _ 8 8 cos sin sin where so that 0ÐBÑ œ F #8B F œ 0ÐBÑ #8B.B ! 8œ" _ 88 ! sin sin 4 1 ' 1 /2 and so that 1ÐBÑ œ F Ð)8Ñ #8B F œ 1ÐBÑ #8B .B ! 8œ" _ ‡‡ ! Î# sin sin " #8 1 ' 1 To find the , use the first expression (“where ”). 8 0 Ð B Ñ œF# 8 B œ F# B F% B F' B â œ' B ! 8œ" _ 8 "#$ sin sin sin sin sin for Fœ" Fœ! 8Á$ $8 To find the , use the second expression (“so that ”). 8 (use formula 11 with and ) F œ B #8B .B + œ #8 , œ " 8 ! Î# " #8 1 ' 1
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