Duffing's equation is a model for a dynamic system that includes a damping term and a nonlinear stiffness term. It most notably describes dynamics of electrical systems, but it has a simple analog as a nonlinear vibrations problem. Derive the non-homogeneous Duffings equation below using Hamilton's Principle. Start from the definition of the kinetic energy of a unit mass, and the virtual work of the springs and damper. Note, the spring force terms are both derivable from an energy function. +cx+kx+vx = F sin(wt)