Classical Dynamics of Particles and Systems · Problem 2-43

Oscillations — Marion & Thornton

Physics — Mechanics · nonlinear-force-potential-motion

Problem

A particle is under the influence of a force

F = -kx + kx^3/\alpha^2

, where

k

and

\alpha

are constants and

k

is positive. Determine

U(x)

and discuss the motion. What happens when

E = (1/4)k\alpha^2