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'' + 2x' + 20x - 5x³ = 0: Verify that the critical points resemble those shown in Fig. 9.4.6.

0 Region ly Region I Region III Region I Region II 2

0 Region ly Region I Region III Region I Region II 2 (2,0) Region V FIGURE 9.4.6. Position-velocity phase plane portrait for the soft mass-and-spring system with m = 1, k = 5, B = 4, and resistance constant c = 2. The (black) separatrices are emphasized.

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