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Unformatted text preview: y ( t ) = 2 e 2 t e 4 t , and it approaches as t . (d) In this problem, the stiFness k = 3 is negative. In the massspring model, this means that the spring forces the mass to move in the same direction as the sign of the displacement is. Initially, the displacement y (0) = 2 is negative, and the mass has no initial velocity. Thus the mass, when released, will move in the negative direction, and the spring will enforce this movement. So, we expect that y ( t ) as t . To nd the actual solution, we solve the auxiliary equation r 2 + 2 r 3 = 0 and obtain r = 3, 1. Therefore, a general solution is given by y ( t ) = c 1 e 3 t + c 2 e t . We nd c 1 and 184...
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 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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