Question

Problem 11 Consider the van der Pol oscillator, (d^(2)x)/(dt^(2))+omega ^(2)x=epsilon(dx)/(dt)(1x^(2)),epsilon>=0. Describe the dynamics when epsilon=0. What is the effect of the right-hand-side when |x| is small? What is the effect of the right-hand-side when |x| is much larger than 1? Based on your answers to the previous questions, explain what you expect to happen for intermediate values of |x|. Sketch the phase plane of the van der Pol oscillator. Check your answer with the Phase Plane App or equivalent software. Is the result surprising? Why or why not?

Name: problem 11 consider the van der pol oscillator d2xdt2omega 2xepsilondxdt1x2epsilon0 describe the dynamics when epsilon0 what is the effect of the right hand side when x is small what is the 46827
Uploaded: 2022-03-16T17:56:42-08:00
Duration: 32 s
Channel: Keerti J
Description: problem 11 consider the van der pol oscillator d2xdt2omega 2xepsilondxdt1x2epsilon0 describe the dynamics when epsilon0 what is the effect of the right hand side when x is small what is the 46827

          Problem 11
Consider the van der Pol oscillator,
(d^(2)x)/(dt^(2))+omega ^(2)x=epsilon(dx)/(dt)(1x^(2)),epsilon>=0.
Describe the dynamics when epsilon=0.
What is the effect of the right-hand-side when |x| is small?
What is the effect of the right-hand-side when |x| is much larger than 1?
Based on your answers to the previous questions, explain what you expect to happen for intermediate values of |x|.
Sketch the phase plane of the van der Pol oscillator.
Check your answer with the Phase Plane App or equivalent software. Is the result surprising? Why or why not?

Added by Jonathon W.

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