MATHEMATICS 317 Solutions to Ass1

MATHEMATICS 317 Solutions to Ass1 - MATHEMATICS 317...

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MATHEMATICS 317 Solutions to Ass. #1 1(a) . ) ( Hence . 0 , 1 ) 0 ( ; , constants ed undetermin for 1 ) ( i.e., , 1 ] (2) Eqn. [from (1) Eqn. ) 2 ( / 2 ) 1 ( / 2 ) ( ) ( ) ( ; ) ( ) ( ) ( 2 2 2 2 2 2 2 j i r j i r j i r j i j i r j i r t t t t t t e e t b a b a b e a ae t b e a y ae x x y x x x x t y t x t t y t x t - - - + = = = + = + + = + = = - = = - = + = + = (b) . 4 ) ( ) ( ) ( 2 ) ( ) ( j i r v a j i r v t t t t e e t t t e e t t - - + = = = - = = 2. (a) ,.... 1 , 0 , 2 0 sin , 1 cos 0 ) ( ; sin ) cos 1 ( ) ( ± = = = = = + - = n n t t t t t t t π v j i v (b) The speed of the particle is given by . cos 2 2 ) ( t t - = v The maximum speed occurs when ,... 1 , 0 , ) 1 2 ( ± = + = n n t 3. . / ) / ( ) / / ( / 2 2 2 2 dt d dt d dt d dt d dt d a a a a a a b × = × + × = 4. . 3 3 3 3 2 2 2 2 2 2 2 2 dt d dt d dt d dt d dt d dt d dt d dt d dt d dt d dt d dt d r r r r r r r r r r r r r r r × = × + × + × = × 5. (a)
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MATHEMATICS 317 Solutions to Ass1 - MATHEMATICS 317...

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