Setting up two degree of freedom vibration absorber equations

[renta]

I'm trying to design a vibration absorber that will reduce the vibration of a machine by about 60%. I found the equations of motion of the machine without the absorber to be..
m1+x2"+ k1*x1+k2(x1-x2)+C2(x1'-x2')=Fo*sin(wt)
and the absorber alone to be..
m1+x2"+k2(x1-x2)+C2(x2'-x1')=0

How do I do a two degree of freedom system (the machine and absorber together)? I have to calculate the natural frequencies and write the equations of motion in matirx form, and find the K and M matrices, form M^(-1)*K, and for designed k2 and c2, find the eigenvalues of M^(-1)*K. I really don't have much experience with this area, can someone please help me?

 

[Greg Bernhardt]

It sounds like you have a good understanding of what needs to be done, but might be having trouble putting it all together. You're right that you need to calculate the natural frequencies and write the equations of motion in matrix form. To do this, you'll need to combine the two equations of motion into one. This can be done by subtracting one equation from the other. Once you have the combined equation, use the method of assumed modes to solve for the natural frequencies and write out the equations in matrix form. After that, you can find the K and M matrices and M^(-1)*K. Finally, you can find the eigenvalues of M^(-1)*K for the designed k2 and c2.

If you're still having trouble, I'd recommend looking for tutorials online that explain how to do a two degree of freedom system. There are lots of resources available and some of them might be better suited for your specific needs. Good luck!