Unformatted text preview: to approach zero displacement point, y = 0. Thereafter, with y ( t ) > 0, the stiFness becomes negative, which means that the spring itself will push the mass further away from y = 0 in the positive direction with force, which increases with y . Thus, the curve y ( t ) will increase unboundedly. ±igure 4.23 con²rms our prediction. 5. (a) Comparing the equation y = 2 y 3 with equation (7) in Lemma 3, we conclude that f ( y ) = 2 y 3 , and so F ( y ) = Z 2 y 3 dy = 1 2 y 4 + C, where C is a constant. We can choose any particular value for C , say, C = 0. Thus F ( y ) = (1 / 2) y 4 . Next, with constant K = 0 and sign “ − ” in front of the integral, equation (11) on page 201, becomes t = − Z dy p 2(1 / 2) y 4 = − Z y − 2 dy = y − 1 + c, 227...
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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 Berkeley.
 Spring '10
 Hald,OH
 Math, Differential Equations, Linear Algebra, Algebra, Equations

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