C please Part II. Writing the equationd²dt²in the form of the system(a)(b)(c)(d)(e)x= x=x²,x = V₁v = x= x²dt2= x(t),x =x = x (t),v²+ W(x) = const for each solution (x(t), v(t)) to system (2),v = v(t),dxFind all the stationary points (x, v) (the points where dt = 0, d = 0).dtFind the corresponding linear system near each critical point.Find the corresponding linear system near each critical point.Draw a phase portrait of the system near each critical point.Draw a phase portrait taking into account the energy conservation,1where the potential energy is given by the antiderivative of -x +x²,x²W(x)2+3(1)(2)

For the non-linear system(c) To find the linear system corresponding to the equilibrium points.Here,…

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Find the corresponding linear system near each critical point.

Glencoe Algebra 1, Student Edition, 9780079039897, 0079039898, 2018

18th Edition

ISBN:9780079039897

Author:Carter

Publisher:Carter

Chapter9: Quadratic Functions And Equations

Section9.7: Solving Systems Of Linear And Quadratic Equations

Problem 3GP

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Question

C please

Part II. Writing the equation
d²
dt²
in the form of the system
(a)
(b)
(c)
(d)
(e)
x= x=x²,
x = V₁
v = x= x²
dt
2
= x(t),
x =
x = x (t),
v²
+ W(x) = const for each solution (x(t), v(t)) to system (2),
v = v(t),
dx
Find all the stationary points (x, v) (the points where dt = 0, d = 0).
dt
Find the corresponding linear system near each critical point.
Find the corresponding linear system near each critical point.
Draw a phase portrait of the system near each critical point.
Draw a phase portrait taking into account the energy conservation,
1
where the potential energy is given by the antiderivative of -x +x²,
x²
W(x)
2
+
3
(1)
(2)

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