3 2. Show that van der Pol's equation+e (a2 - 1)da+ a = 0dtdt2is equivalent to a system in () where y = dx/dt. Here, the value of e indicates thenonlinearity and the strength of the damping in the van der Pol's oscillator. Discusshow the stability of the rest solution (r 0) of van der Pol's equation (equivalently,the origin of the system) depends on the parameter e.

The van der pol's equaton- d2xdt2+ε(x2-1)x'+x=0this ODE subsidiary is a self energized…

Answered: dr +e (x - 1) +x = 0 dt dt?

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dr +e (x - 1) +x = 0 dt dt?

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Fluid Kinematics

The branch of science that deals with objects which are either in motion or stationary are studied under the branch of classical mechanics. Fluid mechanics is a subcategory of classical mechanics that deals with the behavior of fluids at rest (fluid statics) or in motion (posing some velocity). In fluid kinematics, studies focus on the associated motion of fluid particles or groups of particles, and its associated parameters like displacements, velocity, and acceleration without concerning about the forces that caused the motion. All the laws of classical mechanics are applied in the study of fluid kinematics.

Question

2. Show that van der Pol's equation
+e (a2 - 1)
da
+ a = 0
dt
dt2
is equivalent to a system in () where y = dx/dt. Here, the value of e indicates the
nonlinearity and the strength of the damping in the van der Pol's oscillator. Discuss
how the stability of the rest solution (r 0) of van der Pol's equation (equivalently,
the origin of the system) depends on the parameter e.

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