M251ex2(sp00)

# M251ex2(sp00) - 1 m/s Then at time t = π 2 an...

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MATH 251 2nd exam Mar 27, 2000 Name: Student Number: Instructor: Section: There are 7 partial credit questions. In order to obtain full credit for these problems, all work must be shown. Credit will not be given for an answer not supported by work. The point value for each question is in parentheses to the right of the question number. THE USE OF CALCULATORS IS NOT PERMITTED IN THIS EXAMINA- TION. At the end of the examination, the booklet will be collected. 1: 2: 3: 4: 5: 6: 7: Total: Do not write in the box to the left

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MATH 251 -2nd exam- 1. (15 points) Find the function y ( t ) whose Laplace transform is the expression 7 s 2 - 8 s + 12 ( s - 2)( s 2 + 4) . Page 2 of 9
MATH 251 -2nd exam- 2. (15 points) Rewrite the following function f ( t ) in terms of step functions, and Fnd its Laplace transform (it is not necessary to graph the function): f ( t ) = ½ t : t < 2 ( t - 2) 2 : t 2 Page 3 of 9

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MATH 251 -2nd exam- 3. (15 points) A 4 kg mass is hung on a spring with spring constant 1 N/m. At time t = 0 the mass is released from its equilibrium position, moving with an upward velocity of

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Unformatted text preview: 1 m/s. Then at time t = π 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 exam-4. (15 points) Solve the initial value problem y 00 + 4 y =-2 δ ( t-π 4 ), y (0) = 2, y (0) = 0. Page 5 of 9 MATH 251 -2nd exam-5. (a) (10 points) Find the eigenvalues of · 1-2 3-4 ¸ (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 exam-6. (a) (10 points) Find the eigenvalues of · 2-5 1-2 ¸ (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 exam-7. (20 points) Find the solution of the initial value problem ~x = · 1-4 4-7 ¸ ~x ~x (0) = · 3 2 ¸ . Page 8 of 9...
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M251ex2(sp00) - 1 m/s Then at time t = π 2 an...

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