HW3-solution

HW3-solution - Homework #3 solution 1). Surface profile in...

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Homework #3 solution 1). Surface profile in Sine wave; find R a , R q α d l a R l a = 2 0 2 sin let = l dx x l a l x l 0 ) sin( 1 2 2 π = [ ] cos 0 cos cos ) cos ( 0 0 - = = - a x l l a x l d l l a l = a a 2 )] 1 ( 1 [ = - - 2 / 1 0 2 2 2 / 1 2 0 2 ] 2 sin [ ] 2 ] sin [ [ dx l x a R dx l x a R q l q = = Since 2 / 1 0 2 2 ] ) 2 cos 1 ( 2 [ 2 2 cos 1 sin dx x a R x x q - = - = = ( 29 ( 29 [ ] 2 / 1 2 2 / 1 0 2 0 0 0 2 ) 2 sin 2 ( 2 - - - = - a x x a = a a a 2 2 2 2 2 / 1 2 = = Surface profile in cosine wave; find R a , R q dx l a R l a = 2 0 2 cos = - = - = - 2 3 cos 2 cos sin cos 2 3 2 2 3 2 a x a xdx a = a a 2 )] 1 ( 1 [ = - - 2 / 1 2 3 2 2 2 2 / 1 2 0 2 ] 2 cos [ ] 2 ] cos [ [ dx l x a R dx l a R q l q = = Since 2 / 1 2 3 2 2 2 ] ) 2 cos 1 ( 2 [ 2 2 cos 1 cos dx x a R x x q + = + = = ( 29 2 / 1 2 2 / 1 2 3 2 2 0 0 2 2 3 2 ) 2 sin 2 ( 2 - + - = + a x
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HW3-solution - Homework #3 solution 1). Surface profile in...

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