Is this answer possible?harmonic oscillator

[fahd]

hi there

i had my classical mechanics exam today and in that there was a question in which there was a potential energy function V(x) given and we had to find the equilibrium points and the frequency of oscillation near the stable equilibrium point..
the potential energy function was given as the sum of two terms that had powers of x in the denominator.

now when i solved to find the equilibriom points.i.e when i equated
d V(X)/dX=0 i got 2 points one at X=0 and the other a X=2 .

Further i checked for the stability of these equilibrium points by seeing if the second derivative of V(x) was positive or negative.To my surprise when i took the value of the second derivative of V(x) at x=o, the value came out to be infinity which i said since was greater then 0, hence X=0 is a stable equilibrium point...further my frequency of oscillation hence at this pointX=0 came out to be 0
is this possible,,,,,,,,i checked my answer 3ce...and found no mistake...please respond!

 

[mezarashi]

When you have powers in the denominator, check for poles (oscillation points) first by finding the roots of the polynomial in the denominator. It would be better if you combine the two polynomials together first.

Make sure your equilibrium points don't coincide with these.

 

[lightgrav]

The $$\frac{d^2 V(x)}{dx^2}$$ is the kurvature "k" familiar from the oscillator equations.
infinite k should have infinite (not zero) frequency.