What Is the Relationship Between Potential V(x) and Small Vibrations in Physics?

[Oliveman]

Homework Statement

A mass moves under a potential V (x) = V0 cosh (x / x0 ) , where V0 and x0 are constants.
a) Make a sketch of V(x)
b) Find the position of stable equilibrium
c)Show that the frequency of small vibrations about this point is the same as it would be
if the mass was in vibration on a spring of spring constant k =V / x2 .

Homework Equations

The Attempt at a Solution

I'm not really sure how to start as I am not very familiar with the cosh function… help please?

 

[vela]

Do you know the definition of the hyperbolic cosine? If not, start by looking it up.