MATH 251 Midterm: MATH 251 PSU s251Exam 2(fa11)
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Page 1: (c, (b, (a, (a, (d, (d) 8. (a) e (b) f (c) f (d) g (a) (unstable) saddle point (b) unstable improper node (c) asymptotically stable spiral node (d) (stable) center (e) asymptotically stable improper node. This problem is mostly about the expansion, so, failure to expand properly must be penalized. If the squared linear factor is does not produce two terms (-4), if the coef - cients are incorrect (-3) and if the laplace lookup is incorrect (-2). 2u1(t)e (t 1) (cos 3(t 1) sin 3(t 1)) (s + 1)2 + 9(cid:27) There are two important points in this problem. For the e s aspect, if u1(t) does not appear but (t 1) is properly substituted (-2). Failure to appropriately determine the numerators for table lookup (resulting in table lookup error) (-4) table lookup error (-1). Y (s) = e 5t s e 10t 4 s(s + 1)2 e 10t.
