MATH 251 Final: MATH 251 PSU s251Final(sp04)

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turquoisegnu128

15 Feb 2019

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Final exam: a) true; b) true, false; d) true, false, true, a) (t) = t 3; b) c = 3, y (t) = ate 2t + bt2 + ct + d, a) t = 3 (sec); b) = 5 (rad/sec): it is critically damped, y(t) = u1(t)(t 1)e3(t 1, (cid:26) x . 2u3(t)(t 3)e3(t 3) x = (cid:20) 0 1 or. 1 (cid:21) e t: it is an unstable saddle point, = 1 d, a) x(t) = (cid:20) cos t 4 sin t. T = 0: the eigenvalues are = , their eigenfunctions are yn(x) = cn cos nx. , n : yes, = 0 is an eigenvalue. Any nonzero constant function is a corresponding eigenfunc- tion. 1 or or product f (x) sin n x. 2 is an even function): u(x, t) = 2e. 4 e 5 2 t sin x: for m = 0, 1, 2, 3, , am =

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MATH 251 Final: MATH 251 PSU s251Final(sp04)

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