hw7soln

hw7soln - 15.5 f (t ) = 3t 4 e2t u (t ) b) f (t ) = t cos (...

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1 15.5 () 2 22 2 2 2 2 2 2 2 3 2 3 cos 2 30 () cos 30 2sin 30 4 3 1 2 4 33 41 2 4 3 3 2 4 3 32 4 3 ( 2 ) ( 2 ) 2 4 3 ft t t ut s d Fs ds s s d ds s ss s s d ds s d ds s s s s s s =+ ⎛⎞ = ⎜⎟ + ⎝⎠ = + +− = + −+ + = + ++ = + = 2 3 2 61 2 3 8 4 s + a) b) 42 43 2 2 34 2 55 3 2 2 63 18 4 72 t te ut dd ds s ds s ds ds = == + + −− c) 2 2 () 4 1 2 4 1 0 2 4 d t t dt d s dt s s s δ =− d) (1 ) 1 1 2 2( ) 1 2 1 t t f te u t eeut e s + = = = + e) 5 ( ) 2 11 5 5 t u s s = 15.5 cont’d b) 4 4( 1) 4 4 (4 ) 2 ( 1 ) 1 ) 1 2 4 2 4 t t s s gt e ut ee u t Gs e e s e s −− − = + = + c) ( ) 2 2 5cos 2 1 () 5cos 1 2sin 1 5 4 4.99 0.174 4 ht t Hs s s s = + + = + d) [ ] 24 6 ( 2 ) ( 4 ) 6 pt Ps ⎡⎤ ⎢⎥ ⎣⎦ f) 3 3 6 6( 3 ) 1 8 6 1 3 31 31 t t eu t = = g) 12 ( 1 ) (0) 10 n n nn n n n n d t ds t sGs s g g s s − − = = = 15.9 a) () () 2 2 2 4 2 2 2 2 s t tu t u t s e s =
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2 () ( ) 22 2 2 2 2 2 2 cos cos cos sin 11 1 1 1 2 t ttt d gt te t dt et t t sd s d Gs ds ds ss s s s s s −−− = =−− ⎛⎞ ++ ⎜⎟ =+ + ⎝⎠ ++−+ + −+ + + + = 15.10
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hw7soln - 15.5 f (t ) = 3t 4 e2t u (t ) b) f (t ) = t cos (...

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