Assignment_9

Assignment_9 - t x s solution Question 2 Apply separation...

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ME 303 ADVANCED ENGINEERING MATHEMATICS Assignment 9 Question 1 . a) Apply separation of variables to find the displacement ( ) t x s , for the following problem, PDE: 1-D wave eqn 2 2 2 2 2 x s a t s = BCs: () 0 , 0 = t x s collar at 0 = x ( ) 0 , = t L s fixed end at L x = ( 2 a , L , 0 V are specified constants) ICs: motion started by an initial velocity ( ) 0 0 , = x s () 0 0 , V x t s = Note: part of this solution was done in Assignment 8. b) For the same problem as in part (a), what initial velocity would be required such that ( ) t x s , contains only the first eigenfunction? What is the
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Unformatted text preview: ( ) t x s , solution? Question 2 . Apply separation of variables to find the steady state temperature ( ) y x T , for the following problem. PDE: 2-D Laplace 2 2 2 2 = ∂ ∂ + ∂ ∂ y T x T BCs: Insulated along = x and = y ( ) 100 , = y a T ( ) , = b x T where a , b are specified constants Question 3 . Repeat Question 2 if the BCs are changed as follows BCs: Insulated along = x and = y plus ( ) 100 , = y a T ( ) 20 , = b x T y x y x...
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