Classical Dynamics of Particles and Systems · Problem 4-25

Gravitation — Marion & Thornton

Physics — Mechanics · van-der-pol-numerical

Problem

Use numerical calculations to find a solution for the van der Pol oscillator of Equation 4.19. Let

x_0

and

\omega_0

equal 1 for simplicity. Plot the phase diagram,

x(t)

, and

\dot{x}(t)

for the following conditions: (a)

\mu = 0.07

x_0 = 1.0

\dot{x}_0 = 0

t = 0

; (b)

\mu = 0.07

x_0 = 3.0

\dot{x}_0 = 0

t = 0

. Discuss the motion; does the motion appear to approach a limit cycle?