Consider the following nonlinear system expressed in polar form: = r ( r - 7) = -1 Which of these statements is true? Select all that apply. A) All solution trajectories approach either r = 5 or r = 7 in a counterclockwise fashion. B) r = 5 is a semistable limit cycle. C) r = 7 is an unstable limit cycle. D) For 0

Question

Consider the following nonlinear system expressed in polar form:  = r  ( r - 7)
 = -1
Which of these statements is true? Select all that apply.
A) All solution trajectories approach either r = 5 or r = 7 in a counterclockwise fashion. 
B) r = 5 is a semistable limit cycle. 
C) r = 7 is an unstable limit cycle. 
D) For 0 < r < 5, the corresponding solution trajectories spiral toward r = 5 in a clockwise fashion. 
E) For r > 7, the corresponding solution trajectories spiral outward away from r = 7 in a counterclockwise fashion.

Quizplus · Accepted Answer

The Answer of Consider the following nonlinear system expressed in polar form:  = r  ( r - 7)
 = -1
Which of these statements is true? Select all that apply.
A) All solution trajectories approach either r = 5 or r = 7 in a counterclockwise fashion. 
B) r = 5 is a semistable limit cycle. 
C) r = 7 is an unstable limit cycle. 
D) For 0 < r < 5, the corresponding solution trajectories spiral toward r = 5 in a clockwise fashion. 
E) For r > 7, the corresponding solution trajectories spiral outward away from r = 7 in a counterclockwise fashion.

Consider the Following Nonlinear System Expressed in Polar Form