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Unformatted text preview: (e) k = 3 + sin t . Since  sin t  1 For any t , we conclude that k 3 + ( 1) = 2 > , and all the solutions are bounded as t + . (f) Here there is positive damping b = t 2 increasing with time, which results an increasing drain oF energy From the system, and positive constant stifness k = 1. Thus all the solutions are bounded. (g) Negative damping b = t 2 increases (in absolute value) with time, which imparts energy to the system instead oF draining it. Note that the stifness k = 1 is also negative. Thus we should expect that some oF the solutions increase unboundedly as t + . 39. IF a weight oF w = 32 lb stretches the spring by ` = 6 in = 0 . 5 Ft, then the spring stifness must be k = w ` = 32 . 5 = 64 (lb / Ft) . 256...
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This note was uploaded on 03/29/2010 for the course MATH 54257 taught by Professor Hald,oh during the Spring '10 term at University of California, Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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