(Large-amplitude periodic solutions for the forced

Chapter , Problem 4

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(Large-amplitude periodic solutions for the forced mass-spring system with a rubber band) Surprisingly, the equation in Part 3 has a second large amplitude periodic solution for parameter values in the range we are considering. Using the same values of k1, b, , and k2 as in Part 3, search for initial conditions that lead to this large amplitude solution. This is delicate work. You will need to try many different initial conditions and allow the numerical method to work for a long time interval (on the order of 0 t 1000). Then check to see if the solution has approached a periodic solution. To help you in your search, we include Figure 4.43. It is a picture of a square in the first quadrant of the yv-plane. Solutions with initial conditions in the blue bands approach the small-amplitude periodic orbit over the long term. Solutions with initial conditions in the black bands do not approach the small amplitude solution for 0 t 1000. This figure was produced for k1 = 13, k2 = 4, b = 0.01, and = 4, but it should give you some idea of how to start your search with your values of k1 and k2.

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