Question

Assume space and time as discrete and composed of a lattice of oscillators. To simplify, let us consider a single harmonic oscillator modelled as a mass, m connected to a spring with spring constant, k. The total energy of this single oscillator is given by E = K + U. The maximum kinetic energy, K occurs at equilibrium, when U= 0, and the mass is moving with maximum speed vnr. Here the total energy is all in kinetic form and can be written as Kmar- mvmar2 The maximum potential energy, U occurs when A -0 (the mass momentarily comes to rest) and the spring is fully extended to a length Xma Here the total energy is all in potential form (stored in spring) and can be written as Umar kxma2 s. Useful relations: Va A textbook will refer to Imax as the amplitude, A. v, the positon, x can be written as b) Define all of the analogous variables which allow the preceding expression to be cast into the form of the Lorentz contraction and compose a figure which illustrates the idea.

Answer 1