test_2_review

test_2_review - + Ft + G ) e-3 t 7. 4.5 problem 18: c 1 e 3...

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MA 341-001 Test 2 Review Questions S. Schecter March 12, 2008 1. Homogeneous 2nd order linear equations with constant coefcients: Sec. 4.2 problems 4, 16; sec. 4.3, problems 14, 24. 2. Undetermined coefcients: Sec. 4.4 problems 18 and 32, Sec. 4.5 problems 18 and 28. 3. Variation oF parameters: Sec. 4.6 problem 18. 4. Mass-spring systems: Sec. 4.8 problem 2. 5. De±nition oF Laplace transForm: Sec. 7.2 problem 4. 6. Laplace transForms From tables: Sec. 7.3 problems 6 and 10. 7. Inverse Laplace transForms: Sec. 7.4 problems 24 and 26. 8. Solving initial value problems: Sec. 7.5 problem 10. 9. TransForms oF discontinuous Functions: Sec. 7.6 problem 32. 10. TransForms oF delta Functions: Use last homework assignment. 1
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Answers: 1. 4.2 problem 4: c 1 e - 3 t + c 2 te - 3 t 2. 4.2 problem 16: 4 3 e t - 1 3 e 3 t 3. 4.3 problem 14: c 1 e t cos 5 t + c 2 e t sin 5 t 4. 4.3 problem 24: 1 3 sin 3 t + cos 3 t 5. 4.4 problem 18: y p = - 2 t cos 2 t 6. 4.4 problem 32: t ( At 6 + Bt 5 + Ct 4 + Dt 3 + Et 2
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Unformatted text preview: + Ft + G ) e-3 t 7. 4.5 problem 18: c 1 e 3 t + c 2 e-t-t 2 + 4 t 3 + 1 9 8. 4.5 problem 28: e-4 t 60 + 1 12-e t 10-e 2 t 6 + 7 e 3 t 6 9. 4.6 problem 18: c 1 e 3 t + c 2 te 3 t + e 3 t 2 t 10. 4.8 problem 2: y =-1 4 cos 5 t-1 5 sin 5 t = √ 41 20 sin (5 t + φ ) where φ = arctan ( 5 4 )-π =-2 . 246. amplitude = √ 41 20 , period = 2 π 5 , frequency = 5 2 π , passes through equilibrium at t = π-arctan ( 5 4 ) 5 = 0 . 449 seconds. 11. 7.2 problem 4: 1 ( s-3) 2 , s > 3. 12. 7.3 problem 6: 2 ( s +2) 2 +4 + 2 ( s-3) 3 13. 7.3 problem 10: ( s-2) 2-25 (( s-2) 2 +25) 2 14. 7.4 problem 24: 5 e t + 2 e 2 t cos 3 t-5 e 2 t sin 3 t 15. 7.4 problem 26: 1-3 2 t 2 + 6 e 2 t 16. 7.5 problem 10:-t-e-2 t + 2 te-2 t + e 2 t 17. 7.6 problem 32: cos t-sin 2 t-(2 sin t ) u ( t-2 π ) + (sin 2 t ) u ( t-2 π ) 2...
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This test prep was uploaded on 03/31/2008 for the course MA 341 taught by Professor Schecter during the Spring '08 term at N.C. State.

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test_2_review - + Ft + G ) e-3 t 7. 4.5 problem 18: c 1 e 3...

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