Question

A potential energy function is given by U(x) = x^(−8)e^x^2 . Let’s only focus on the region where x > 0.

a) Find the position where the potential energy is a minimum

b) For small oscillations around this minimum, what is the angular frequency ω?

c) At what distance (either to the left or right) from the equilibrium point is the exact value of the force (derived from the full potential) more than 10% different from the force corresponding to the second order expansion of the potential used in part b?

I only need part c. I have done the taylor expansion and found the equation for exact force but I don't know how to get the smallest distance for 10% change.

Answer 1