midterm3-sample.pdf - MIDTERM 3 – MATH 2065 – Fall 2013 – Version 1 Name Justify your answers to receive full credit No notes formula sheets

# midterm3-sample.pdf - MIDTERM 3 – MATH 2065 – Fall 2013...

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MIDTERM 3 – MATH 2065 – Fall 2013 – Version 1 Name: Justify your answers to receive full credit. No notes, formula sheets, phones allowed. Basic scientific calculator allowed. Good luck! Time: 50 minutes; Points: 100 (1) (7 points) 3 0 1 0 - 1 0 2 4 2 1 8 9 4 - 1 3 5 = (2) (13 points) A = 2 4 1 0 - 1 2 1 2 3 0 2 3 5 . (a) Fill in the missing entries in the cofactor matrix Cof( A ). (You don’t have to show your work in this step) Cof( A ) = 2 6 6 6 6 4 2 - 3 5 1 1 3 7 7 7 7 5 (b) Use your answer and the adjoint inverse formula to find the inverse of A . 1
(3) (6 points) Write the indicial polynomial Q ( s ) that would be used to solve the following Cauchy-Euler equation. (Do not solve the equation.) 3 t 2 y 00 + 2 ty 0 - 7 y = 0 Q ( s ) = (4) (7 points) A mass attached to a spring and dashpot is pulled up 1 foot from equilibrium and released. Its resultant equation of motion is y = (1 - 3 t ) e - 2 t After release, does the mass ever cross equilibrium again? Justify your answer. (5) (13 points) A 2 kg mass is attached to a spring with spring constant k = 5N/m and an accompanying dashpot. The damping force of the dashpot is 6 N when the velocity of the body is 1 m/s.

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