MT_2_Math_33B_W09

MT_2_Math_33B_W09 - Mathematics 33B Midterm 2 Instructor D...

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Mathematics 33B - Midterm 2 Instructor : D. E. Weisbart February 27, 2009 NAME (please print legibly): Your University ID Number: Your Discussion Section and TA: Signature: There are FIVE questions on this examination. Calculators, notes and books may not be used in this examination. Full credit may not be given if insufficient work is shown. QUESTION VALUE SCORE 1 20 2 20 3 20 4 20 5 20 TOTAL 100 1
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1. (20 points) a) Find the general solution of the equation x 00 + 5 x 0 + 6 x = 0. b) Find the general solution of the equation x 00 + 5 x 0 + 6 x = 52 cos 2 t . Make sure to show your work. 2
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2. (20 points) a) Find the general solution of the equation x 00 - 4 x 0 + 4 x = 0. b) Find the general solution of the equation x 00 - 4 x 0 + 4 x = e 2 t . Make sure to show your work. 3
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3. (20 points) a) If an undamped mass-spring system starts at rest and is subjected to a force F ( t ) = 10 e - t , the displacement of the mass at time t is a solution to the initial value problem x 00 + 4 x = 10 e - t , x (0) = 0 , x 0 (0) = 0 . Find x ( t ).
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