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Writing Matrix Equations and Programs for Spring Mass System

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.

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Solution Preview

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 ...

Solution Summary

This solution provides a written description and a Matlab program for finding the positions of blocks in a spring mass system.