Having issues with a seemingly simple problem

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In summary, a particle of mass m is subjected to a force that is inversely proportional to the cube of its distance from the origin. If the particle is initially at rest at a distance x_0 from the origin, the equations of motion can be set up using Newton's Second Law. One possible solution is to use conservation of energy, taking into account both potential and kinetic energy.
  • #1
Xyius
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Homework Statement


A particle of mass m is repelled from the origin by a force inversely proportional to the cube of its distance from the origin. Set up and solve the equations of motion if the particle is initially at rest at a distance [itex]x_0[/itex] from the origin.

(This is one dimensional motion)

Homework Equations


Newtons Second Law to set up the equation of motion


The Attempt at a Solution


The first part is simple. I just had..
[tex]m \ddot{x}=\frac{k}{x^3}[/tex]

And this part is right. I am having trouble solving it however. I know it is just a method from my differential equations course but I am having trouble for some reason!
 
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  • #2
Try conservation of energy - potential + kinetic.
 

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