The equations used to generate this model use the following assumptions:
These assumptions cause the equation to be true for the oscillation of a spring that is not moving, which is a complete contradiction in itself, but it produces a reasonable approximation from which to start.
This model uses 6 masses connected together by a series of springs. MATLAB is used to solve the equations and generate the waveform, in particular, the function ode45 solves the equations.
This models a string being plucked - at least this is the aim, in actual fact it makes a sort of 'bung' sound, more reminiscent of a rubber band round a cardboard box. But this is perhaps not surprising, since a decent physical modelling instrument will take months to develop by a trained expert, and this is about as far as you can get in a few poor 4th year lab sessions...