Consider the simple pendulum x_ 1 = x2; x_ 2 = b ml2 x2 g l sin (x2) : Using the total energy as the candidate Lyapunov function, show that [00] is an asymptotically stable equilibrium point. Find an estimate of the region of attraction of [00] so that the projection of the region of attraction on the x1 dimension includes the interval (pi; pi)

its b

step-by-step explanation:

the y will be in still but your answer will be y x 3

step-by-step explanation:

jk: )

(0,,,0)

step-by-step explanation:

the table of x and y values is shown in the attached pic(part of question)

we have to decide according that graph

given points are (0, 0) (–1, 0), (2, 0)

when we graph these points on graph they show an increasing line as shown in the attached pic

hello from mrbilldoesmath!

answer:

(7 x + 6 y) (49 x^2 - 42 x y + 36 y^2)

discussion:

the trick is to recognize that 343 = 7^3 and 216 = 6^3 and, in general,

a^3 + b^3 =   (a + b) (a^2 - a b + b^2).

in our case

343x^3+216y^3   =   (7x)^3 + (6y)^3

so take a = 7x and b = 6y in the above equation to get the answer.

you,

mrb