Fermi, Pasta, Ulam, and Tsingou simulated the vibrating string by solving the following discrete system of nearest-neighbor coupled oscillators. We follow the explanation as given in Richard Palais 's article. Let there be N oscillators representing a string of length ℓ ℓ with equilibrium positions p j = j h , j = 0 , … … , N − − 1 , where h = ℓ ℓ / ( N − − 1 ) is the lattice spacing. Then the position of the j -th oscillator as a function of time is X j ( t ) = p j + x j ( t ) , so that x j ( t ) gives the displacement from equilibrium. FPUT used the following equations of motion: