[spring system] 3 degree of freedom system and its properties

1. Dec 11, 2013

renvox

Hello, I was given the attached 3 degree of freedom spring system with the purpose of analyzing it.

I came up with the following equation of motion
and then I ran Matlab to calculate the corresponding natural frequencies and mode shapes using eigenvalues and eigenvectors; I was asked to see what happens when value of stiffness k_12 is changed. This is the plot of the value k12 against the natural frequencies.

The problem is that I do not know WHY values of natural frequencies are insensitive at low values of k12 and why both the 1st and 2nd natural frequencies are insensitive to changes in k12 when values are large (first two level off and the third one seems to go to infinity).

I assume it has something to do with the equation for force due to a spring between 2 masses but I cannot figure it out. That is why I ask for your help - thanks in advance.

2. Dec 12, 2013

tiny-tim

hello renvox!
if k12 is a weedy little thing, why should changing it make any noticeable difference?
what are the three eigenvectors (the three modes of oscillation)?