Q14E - Fundamentals Of Differential Equations And Boundary Value Problems

Question

Redo Problem 12 with F = 0.65. What kind of behavior does the solution exhibit?

Step-by-Step Solution

Answer

By using the software the Poincare maps are plotted and the solution is sub harmonic by\(\frac{{{\bf{4\pi }}}}{{\bf{\gamma }}}\).

Step 1: Sketch the Poincare map

Here the equation of (7) is:

 

\({\bf{x''(t) + bx' - x(t) + }}{{\bf{x}}^{\bf{3}}}{\bf{ = Fsin\gamma t}}\)

 

Put the given values when b = 0.3,\({\bf{\gamma }} = 1.2\), and F =0.65.

Step 2: Sketch for \({{\bf{t}}_{\bf{0}}}\) =0, 15, and 50 respectively

Thus, the Poincare maps are plotted and the solution is sub harmonic by\(\frac{{{\bf{4\pi }}}}{{\bf{\gamma }}}\).