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## Homework Statement

Particle mass m is moving along the x-axis.

The particle is attracted to the principle axis O to measure power

**mk/x^2**when

**x>a**

and repels the O with measure power

**mka/x^3**when

**0<x<a**, where

**a,k>0**

i) Find the potential energy of the particle

ii)The particle is released from rest at 2a from O. Describe the movement to perform the particle and show that the particle will stand briefly when x=a/sqrt2

## The Attempt at a Solution

i) I tried to find the potential energy by integrating the function of power:

.............mk / x ^ 2 , x> a

F (x) =

.............mka / x ^ 3 , 0 <x <a

using the relation F (x) = - dU / dx, but the integral constant C if assume that U (O) = 0, goes infinity (oo).

I still can not design the function of potential energy which found that likely have the form:

..............-mk / x , x> a

U (x) =

...............mka / x ^ 2 , 0 <x <a

ii) For the second question I can not think of anything.

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