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Unformatted text preview: 1 m/s. Then at time t = 2 , an electromagnet is turned on, which exerts an upward external force sin t on the mass. Set up and solve the initial value problem for u ( t ), the displacement of the mass from equilibrium at time t. Page 4 of 9 MATH 251 2nd exam4. (15 points) Solve the initial value problem y 00 + 4 y =2 ( t 4 ), y (0) = 2, y (0) = 0. Page 5 of 9 MATH 251 2nd exam5. (a) (10 points) Find the eigenvalues of 12 34 (b) Find the general solution of ~x = A~x . (c) Describe the type and stability of the critical point ~x = ~ 0. Page 6 of 9 MATH 251 2nd exam6. (a) (10 points) Find the eigenvalues of 25 12 (b) Find the general solution of ~x = A~x . (c) Describe the type and stability of the critical point ~x = ~ 0. Page 7 of 9 MATH 251 2nd exam7. (20 points) Find the solution of the initial value problem ~x = 14 47 ~x ~x (0) = 3 2 . Page 8 of 9...
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 Spring '08
 CHEZHONGYUAN
 Math, Differential Equations, Equations, Partial Differential Equations

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