Hi Everyone,(adsbygoogle = window.adsbygoogle || []).push({});

I think I've solved the equations of motion for a particle in this one-dimensional potential -

V(x) = -k/(a-x) - k/(a+x) with |x| < a, a is real +ve, x is real.

K is a constant of suitable dimension.

It's a charge between two like charges with separation 2*a.

I start with the force equation

m*x'' = -4*a*k*x / (a^2 - x^2)^2

(Using ' to indicate differentiation wrt time)

I can integrate this to get

m*x' = sqrt(2*k*a)/sqrt(a^2 - x^2)

This ought to be textbook example, can anyone point me to an authoritative solution or come up with x ?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Homework Help: Interesting oscillator potential

**Physics Forums | Science Articles, Homework Help, Discussion**