1. find the phase space of the harmonic oscillator
x_double_dots + (w^2)x = 0
and the one parameter group of diffeomorphisms gt . also find two different
type of orbits. are these orbits phase curves?
2. consider the nonlinear pendulum
x_double_dots + sin(x) = 0
describe four different types of phase curves for the nonlinear pendulum.

as we probably am aware that our atmosphere or air have various levels, each level has different gasses, and each gas has another porousness. at the point when the light originates from lower porousness to higher penetrability, it alters its course. with the goal that implies that when the light originates from the moon to the earth, it alters it's course a lot more occasions. it essentially implies that the state of the light piece of the moon is changed on the earth.

not copied too! hope this !

joke:

h o h o hope you have a merry christmas!

find the surface area of the sphere to the nearest square unit. use a calculator.

a. 254 in.2

b. 64 in.2

c. 127 in.2

d. 1,018 in.2