ex07_solutions

Solutions

For small initial displacements, the anharmonic oscillator behaves like the harmonic one, but the effect of the third order term can be seen by increasing s. With the third order term accounted for, the force takes on larger values and the oscillation speeds up.

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$(*1*)deq := m x''[t] + k x[t] + ϵ x[t]^30 ; k = 0.5 ; s = 2 ; ... x[t]/.sol1, x[t]/.sol2}, {t, 0, T}, PlotStyle {Hue[0], Hue[0.6]}, PlotPoints100]$

[Graphics:../HTMLFiles/ex07_solutions_38.gif]

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Note that for ParametricPlot, one layer of the solution list has to be truncated (flattened) using the Part function.

In[43]:=

$(*2*)deq1 = m_1x_1''[t]  -k_1x_1[t] - k_2 (x_1[t] - x_2[t]) ; deq2 = ... {t, 0, T}] ParametricPlot[{x_1[t]/.sol, x_2[t]/.sol}, {t, 0, T}, PlotPoints300]$

[Graphics:../HTMLFiles/ex07_solutions_41.gif]

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[Graphics:../HTMLFiles/ex07_solutions_43.gif]

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Created by Mathematica (April 10, 2007)