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Chapter 5: Q14E (page 304)

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

Short Answer

Expert verified

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

Step by step solution

01

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.

02

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

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

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