13. Consider the spring mass system (see attached file) (a simple model of a short polymer molecule). The blocks are free to move but only along the x-axis. The springs connecting adjacent blocks have spring constant k1, while the two outer springs have stiffness k2. All the springs have a rest length of one. (a) Write the matrix equation for the equilibrium positions of the blocks. (b) Write a program that plots the total length of the system as a function of k1/k2.
(See attached file for full problem description)
As we address only the equilibrium, we can take the leftmost block at x= 0, and the other three blocks at x1, x2, and x3, respectively, from left to right.
Then, the equations of equilibrium at x1, x2, and x3 ...
This solution provides a written description and a Matlab program for finding the positions of blocks in a spring mass system.