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'' + 4x - 5x³ + x⁵ = 0: The idea here is that terms through the fifth degree in an odd force function have been retained. Verify that the critical points resemble those shown in Fig. 9.4.14.

Transcribed Image Text:

XX -2 2 18 FIGURE 9.4.14. The phase portrait for Problem 16.