s251ex2(fa07)

# s251ex2(fa07) - neutrally stable(b-= t t C t t C t x cos...

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MATH 251 Exam 2 November 12, 2007 ANSWER KEY 1. (a) III (b) I (c) II (d) IV (e) V (f) VI 2, B 3. A 4. C 5. B 6. (a) y = 3cos(2 t ) - 2sin(2 t ), has amplitude R = 13 2 2 2 1 = + C C . (b) ω = ω 0 = 2 (c) The system must be critically damped or overdamped: γ ≥ 8. 7. (a) + = - s s e s F s 3 1 ) ( 2 3 (b) f ( t ) = e -2 t cos( t ) - 2 e -2 t sin( t ) 8. ( ) 6 2 3 3 2 2 ) ( 3 1 3 ) ( + - - - + + = t t t e e t u e t y 9. (a) The eigenvalues are purely imaginary. Therefore, the critical point is a center , and it is stable (or
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Unformatted text preview: neutrally stable). (b) + -= t t C t t C t x cos sin 2 sin cos 2 ) ( 2 1 10. (a) t t e C e C t x 2 2 1 1 4 1 1 ) ( + =-(b) β = 6 11. (a) (0,0), (-1,1), (1,-1) (b) It is a spiral point ; asymptotically stable....
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