Degrees of Freedom y(x) -

A function y(x) summarizes the degrees of freedom for the string. This is because we must give the y-location for each segment in order to know the configuration of the string. (We already know the x location for each segment because the segments do not move along x.) By sketching a function y(x), we get a picture of the string and thus determine exactly what our system looks like at a given time, precisely what the degrees of freedom are supposed to do.