Find the displacements u1, u2, ... u100 of 100 masses connected in a row by identical springs, with spring constant c = 1. Consider the following three types of force functions:
(a) Constant force: f1 = . . . = f100 = .01;
(b) Linear force: fi = .0002i;
(c) Quadratic force: fi = 6 ∙ 10-6 i (100 - i).
Also consider two different boundary conditions at the bottom:
(i) Spring 101 connects the last mass to a support.
(ii) Mass 100 hangs free at the end of the line of springs.
Graph the displacements and elongations in all six cases. Discuss your results: in particular, comment on whether they agree with your physical intuition.