Vibrating Reed Composed of a 2D Numerically Modeled Solid Lattice

I have deliberately allowed slider variable ranges that can result in a break up of the solid. It that happens, the learner just needs to refresh the page, which in Windows means hitting the F5 key, and then choose less radical parameters. In this simulation the bonding is done with a Lennard-Jones (LJ) potential. LJ potentials have extremely large repelling forces when the particles get too close and only moderate attractive forces when the particles are farther apart. The reason for the strong difference between close and far range forces is the Pauli Exclusion principle which requires minimal overlap between electron wave functions. The LJ potential is of the form
V(r)=4VLJ[(sigma/r)^2b-(sigma/r)^b]
where VLJ is the potential minimum, sigma is a length scaling parameter, r is the particle separation, and b=6 for this simulation. The solid is initially set up so that all the particles are separated by a distance that causes the nearest neighbor forces to be zero. The force between a site and its second nearest neighbor is not initially zero. Also the setup anchors the left column discs so that they can't move in either the vertical or horizontal directions. An obvious result of that set up is that alternate rows of particles have to be staggered by 1/2 the spacing in the horizontal direction and the vertical spacing of rows is squareroot(3)/2 times the horizontal spacing of particles. The initial configuration is thus that of a perfectly regular crystal. In order to initiate vibration of the reed, the right end of the solid is deflected downward using the equation y(x)=a*x*x/2 where maximum deflection, yMax, at the end is yMax=1/2*a*xEnd^2 which means that a=2*yMax/xEnd^2. This reduces the spacing between the discs in the bottom row and increases the spacing between the discs in the top row. As shown in the graphic the concave edge of the solid has extensive restoring forces and the convex side has contractive restoring forces. The color bar shows the magnitudes of these forces. The learner will also note some much more rapid and closer range oscillations between particles. These are just the nearest neighbor frequencies of the LJ potential. This simulation will usually take a few minutes to complete so I have provided a movie that can be played up to the time to which the simulation has progressed.