{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

s251final(fa03)

# s251final(fa03) - MATH 251 Fall 2003 Final Exam ANSWERS 1 B...

This preview shows page 1. Sign up to view the full content.

MATH 251 Fall 2003 Final Exam Decemebr 15, 2003 ANSWERS: 1. B 2. B or C 3. C 4. A 5. B 6. A 7. (a) Critical points are (1 , 1) and (1 , - 1) (b) (1 , 1) is unstable (a saddle point); (1 , - 1) is unstable (a spiral point/spiral source) 8. y ( t ) = - 7 6 e - 3 t + 1 2 e t - 1 3 t + 2 3 9. m = 2 , γ = 6 , k = mg L = 4 (a) 2 u ” + 6 u 0 + 4 u = 0 or u ” + 3 u 0 + 2 u = 0 , u (0) = 0 , u 0 (0) = 5 Solution: u ( t ) = 5 e - t - 5 e - 2 t (b) (Trick question!) The system is overdamped . There is no oscillation, therefore, there is no quasi- period. Also acceptable: quasi-period = . 10. (a) y = - 3 , 0 , 3 (b) y = - 3 is asymptotically stable; y = 0
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern