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23 Nov 2019
<p>Assume thatx(t)=b9cos(ω<sub>o</sub>t)+u(t) is a solutionof the vander Pol Equation 4.19. Assume that the dampingparameter μ is small and keep terms in u(t) tofirst order in μ. Show that b= -2a and u(t)=-(μa<sup>3</sup>/4ω<sub>o</sub>)sin(3ω<sub>o</sub>t)is a solution. Produce a phase diagram of x' vs x and produce plotsof x(t) and x'(t) for values of a=1,ω<sub>o</sub>=1, andμ=0.05.</p>
<p>equation 4.19</p>
<p>x''+μ(x<sup>2</sup>-a<sup>2</sup>)x'+ω<sub>o</sub><sup>2</sup>x=0</p>
<p>Assume thatx(t)=b9cos(ω<sub>o</sub>t)+u(t) is a solutionof the vander Pol Equation 4.19. Assume that the dampingparameter μ is small and keep terms in u(t) tofirst order in μ. Show that b= -2a and u(t)=-(μa<sup>3</sup>/4ω<sub>o</sub>)sin(3ω<sub>o</sub>t)is a solution. Produce a phase diagram of x' vs x and produce plotsof x(t) and x'(t) for values of a=1,ω<sub>o</sub>=1, andμ=0.05.</p>
<p>equation 4.19</p>
<p>x''+μ(x<sup>2</sup>-a<sup>2</sup>)x'+ω<sub>o</sub><sup>2</sup>x=0</p>
