Unformatted text preview: ± =. 1 ,. 2 ,. 3 ,. 4 and plot the solutions of the above initial value problem for 0 ≤ t ≤ 20. Estimate the amplitude of the spring. Experiment with various ± < 0. What appears to happen to the amplitude as ± → ∞ ? Let μdenote the ﬁrst time the mass reaches equilibrium after t = 0. Estimate μwhen ± =. 1 ,. 2 ,. 3 ,. 4. What appears to happen to μas ± → ∞ ? 3. Given that a certain nonlinear hard spring satisﬁes the initial value problem ( u 00 + 1 5 u + ± u + 1 5 u 3 ) = cos ωt u (0) = 0 , u (0) = 0 plot the solution u ( t ) over the interval 0 ≤ t ≤ 60 for ω = 0 . 5 , . 7 , 1 . , 1 . 3 , 2 . 0. Continue to experiment with various values of ω , where 0 . 5 ≤ ω ≤ 2 . 0, to ﬁnd a value ω * for which  u ( t )  is largest over the interval 40 ≤ t ≤ 60....
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 Fall '09
 Robert Hooke, Nonlinear Springs

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