How to Approximate Potential Energy for a Linear Harmonic Oscillator?

[neelakash]

Homework Statement

Find the linear harmonic oscillator approximation for potential energy function:

\ V=\frac{a}{x^2}+\ b\ x^2

Homework Equations

The Attempt at a Solution

The 2nd term will be present in the expression of V(approx).But what about the first term. Should we make it {1+(x-1)} and expand binomially?But that would involve two points of eqlbm---one is 0 and the other is 1...

Can anyone please help?

 

[Shooting Star]

You have to find the minimum first. If both a,b>0, then the minima occur at x= +-(a/b)^1/4. Take the +ve value, say. Expand the function as a Taylor series around that point and retain up to the x^2 term.

Note that the function is not defined at x=0, and approaches infinity as x tends to zero. Why were you thinking of x=0 as an equilibrium point?

 

[neelakash]

Why were you thinking of x=0 as an equilibrium point?

Yes,I really made a mistake in undestanding the problem.Now, I can do it.Thank you very much.