Classical Dynamics of Particles and Systems · Problem 4-1
Gravitation — Marion & Thornton
Physics — Mechanics · nonlinear-potential-springs
Problem
Refer to Example 4.1. If each of the springs must be stretched a distance d to attach the particle at the equilibrium position (i.e., in its equilibrium position, the particle is subject to two equal and oppositely directed forces of magnitude kd), then show that the potential in which the particle moves is approximately
U(x)≅(kd/l)x2+[k(l−d)/4l3]x4