Ashley H.

asked • 04/02/18

If I have been given a graph of potential energy, how do I sketch typical trajectories in the phase plane?

The particle is moving in the x-axis under the action of a conservative force with a potential
energy V (x).

1 Expert Answer

By:

Ashley H.

Sorry but I think you have misunderstood the question. How am I supposed to do this when I have initially been given no values or equation of the line, but simply a sketch of the potential energy graph. Also, I have no idea what a phase plane is and what I'm supposed to be drawing, so if you could help with that two it would be great
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04/03/18

Richard P.

tutor
The expression phase plane normally means a plot of momentum (p) vs  position (x).
For one conservative one dimensional problems one has the relation   
 
E =  p^2 /2m + V(x)  , were m is the mass of the particle and E is the total conserved energy,
 
This equation can be considered an implicit relation between p and x  (parameterized by E)
Thus for a given E,  the equation determines a curve in the plane.
 
 
It is possible that the expression phase plane is being used in some other context unknown to me.,
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04/03/18

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