s251ex2(su03)

s251ex2(su03) - e-t +2 sin 2 t . 8. (a) X ( t ) = C 1 1-1...

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MATH 251 Summer 2003 Exam 2 July 24, 2003 ANSWERS: 1. (d); 2. (a); 3. i. F, ii. F, iii. T; 4. (a) Y ( t ) = ( A 2 t 2 + A 1 t + A 0 ) + t 2 ( B 1 t + B 0 ) e - 2 t + ( C 1 t + C 0 ) cos3 t + ( D 1 t + D 0 ) sin 3 t ; (b) y ( t ) = C 1 e - t + C 2 e t - 3 2 te - t . 5. (a) u 00 + 4 u 0 + 20 u = 0 , u (0) = 0 , u 0 (0) = 2 ; (b) u ( t ) = 1 2 e - 2 t sin 4 t ; (c) μ = 4 rad/sec. 6. f ( t ) = (1 - u 2 ( t )) t 2 + ( e 3 t - t ) u 2 ( t ) ; F ( s ) = 2 s 3 - e - 2 s s 3 ( 2 + 5 s + 6 s 2 ) + e 6 - 2 s s - 3 . 7. y ( t ) = e - t cos2 t + 1 2 e - t sin 2 t + 3 2 u 2 π ( t )
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Unformatted text preview: e-t +2 sin 2 t . 8. (a) X ( t ) = C 1 1-1 e-3 t + C 2 5 2 e 4 t ; (b) = 5 . 9. X ( t ) = 5 e t sin 3 t-2 e t cos3 t 5 e t cos3 t + 2 e t sin3 t ....
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