Please solve question 12 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 crit- ical points of the equivalent first-order system. 12. x" + 20x – 5x³ = 0: Verify that the critical points resem- ble those shown in Fig. 6.4.4. (-2, 0) 2 (2, 0) -5 -4 –3 –2 –1 0 1 2 3 4 5 FIGURE 6.4.4. Position-velocity phase plane portrait for the soft mass-and-spring system with m = 1, k = 4, and B = 1 > 0. The separatrices are emphasized.
Please solve question 12 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 crit- ical points of the equivalent first-order system. 12. x" + 20x – 5x³ = 0: Verify that the critical points resem- ble those shown in Fig. 6.4.4. (-2, 0) 2 (2, 0) -5 -4 –3 –2 –1 0 1 2 3 4 5 FIGURE 6.4.4. Position-velocity phase plane portrait for the soft mass-and-spring system with m = 1, k = 4, and B = 1 > 0. The separatrices are emphasized.
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Transcribed Image Text:Please solve question 12
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 crit-
ical points of the equivalent first-order system.
12. x" + 20x – 5x³ = 0: Verify that the critical points resem-
ble those shown in Fig. 6.4.4.
(-2, 0) 2
(2, 0)
-5 –4 –3 –2 –1 0 1 2 3 4 5
FIGURE 6.4.4. Position–velocity phase plane portrait
for the soft mass-and-spring system with m = 1, k = 4,
and B = 1 > 0. The separatrices are emphasized.
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