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Question 1: (A circular limit cycle) Consider x¨+ ax·(x2 +x·2 -1) + x = 0, where a > 0.
i) Find and classify all the fixed points.ii) Show that the system has a circular limit cycle, and find its amplitude and period.iii) Determine the stability of the limit cycle.iv) Give an argument which shows that the limit cycle is unique, i.e., there are no other periodic trajectories.
Question 2: Sketch the phase portrait for each of the following systems. (As usual, r, θ denote polar coordinates.)
7.1.1 r· = r3 - 4r, θ = 1 7.1.2 r· = r(1 - r2 )(9 - r2), θ·=17.1.3 r· = r(1- r2 )(4 - r2), θ· = 2 - r2 7.1.4 r· = r sin r, θ·= 1
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During the first part of a trip, a conoeist travels 82 miles at a certian speed. The canoeist travels 36 miles on the second part of the trip at a speed 5mph slower. The total time for the trip is 3 hrs. What was the speed on each part of the trip..
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2800 people were surveyed about their recent purchases. 715 of those people surveyed bought a television within the last year
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a movie theater sells popcorn in small medium large and jumbo sizes. the customers of the first show purchase 4 small
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A walkway forms the diagonal of a square playground. The walkway is 24in long. To the nearest tenth of a Meter, how long is a side of the playground?
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