5. The van der Pol equation is a model of an electronic circuit that arose back in the days of vacuum tubes: d²y dt²-(1-y²) dy dt + y = 0 Given the initial conditions y(0) = 1 and y'(0) = 1. Solve this equation for t from 0 to 20 using Euler's method with a step size of 0.1. Plot y(t) and y'(t) versus t on the same graph. Also, plot the phase-plane trajectory. Describe the attractor state (Is it a point? An orbit?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
5. The van der Pol equation is a model of an electronic circuit that arose back in the days of
vacuum tubes:
d²y
dt2-(1-y²) a
dy
dt
+y=0
Given the initial conditions y(0) = 1 and y'(0) = 1. Solve this equation for t from 0 to 20 using
Euler's method with a step size of 0.1. Plot y(t) and y'(t) versus t on the same graph. Also,
plot the phase-plane trajectory. Describe the attractor state (Is it a point? An orbit?
Transcribed Image Text:5. The van der Pol equation is a model of an electronic circuit that arose back in the days of vacuum tubes: d²y dt2-(1-y²) a dy dt +y=0 Given the initial conditions y(0) = 1 and y'(0) = 1. Solve this equation for t from 0 to 20 using Euler's method with a step size of 0.1. Plot y(t) and y'(t) versus t on the same graph. Also, plot the phase-plane trajectory. Describe the attractor state (Is it a point? An orbit?
Expert Solution
trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 4 steps with 6 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,