Consider the well-known problem of a cart of mass m moving along the x axis attached to a spring (force constant k), whose other end is held xed. if we ignore the mass of the spring, then we know that the cart executes simple harmonic motion with angular frequency ! = p k=m. 1. assuming, that the spring has mass m, that it is uniform and stretches uniformly, show that its kinetic energy is 1 6mx_ 2. (as usual x is extension of the spring from its equilibrium length.) 2. write down the lagrangian for the system of cart plus spring. write down the lagrange equation of motion. find the frequency of the small oscillations.