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FeDeX_LaTeX
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Homework Statement
The equation of motion of a particle moving in a straight line is
##x'' - x + 2x^3 = 0##
and ##x = \frac{1}{\sqrt{2}}, x' = u > 0## at ##t = 0##. Identify the singular points in the phase plane and sketch the phase trajectories. Describe the possible motions of the particle, indicating the ranges of u for which these motions occur.
The attempt at a solution
I really can't seem to get started on this question -- where are the singular points here, and how might I identify them? The co-efficient of x'' is 1, so it doesn't seem like I can divide by anything useful. I can't set a first derivative equal to zero, because there aren't any in this equation. Is there a form in which I have to rewrite this to get something useful out of it?
The equation of motion of a particle moving in a straight line is
##x'' - x + 2x^3 = 0##
and ##x = \frac{1}{\sqrt{2}}, x' = u > 0## at ##t = 0##. Identify the singular points in the phase plane and sketch the phase trajectories. Describe the possible motions of the particle, indicating the ranges of u for which these motions occur.
The attempt at a solution
I really can't seem to get started on this question -- where are the singular points here, and how might I identify them? The co-efficient of x'' is 1, so it doesn't seem like I can divide by anything useful. I can't set a first derivative equal to zero, because there aren't any in this equation. Is there a form in which I have to rewrite this to get something useful out of it?