MATH 2065 Midterm: MATH 2065 LSU f05 1Exam 3a
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Answer each of the questions on your own paper. Put your name on each page of your paper. Be sure to show your work so that partial credit can be adequately assessed. Credit will not be given for answers (even correct ones) without supporting work. Nd the rst t > 0 for which y(t) = 0. Carefully sketch the graph of your solution for the interval 0 t 2 . Applying the laplace transform to the di erential equation gives s2y (s) sy(0) y (0) + 2sy (s) + 10y (s) = 0. Substituting the initial conditions y(0) = 0, y (0) = 6 and solving for y (s) gives. Taking the inverse laplace transform (formula c. 2. 9) gives y(t) = 2e t sin 3t. This equation represents underdamped motion since the discriminant of the equation is d = 22 40 = 36 < 0.
