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# Writing Matrix Equations and Programs for Spring Mass System

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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)

https://brainmass.com/physics/atoms-molecules/writing-matrix-equations-programs-spring-mass-system-118961

#### Solution Preview

(a)
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.

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