Question: In each of Problems 12 through 16, a second-order equation of the form x'' + f (x, x') = 0, corresponding to a certain mass-and-spring

In each of Problems 12 through 16, a second-order equation of the form x'' + f (x, x') = 0, corresponding to a certain mass-and-spring system, is given. Find and classify the critical points of the equivalent first-order system.

x'' + 20x - 5x3 = 0: Verify that the critical points resemble those shown in Fig. 9.4.4.

5 4 3 (-2,0)2 1 0 E 4 E 4 44E=4 (2,0)

5 4 3 (-2,0)2 1 0 E 4 E 4 44E=4 (2,0) E 0. The separatrices are emphasized.

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