Finding Transfer Functions for Mechanical Systems

[jrand26]

Hi guys

I'm an electrical engineer and we're currently doing some control stuff which involves mechanical systems. I'm having particular trouble with a two body problem, I understand how to do the free body diagram and get the equations of motion, but I'm not sure how to get the transfer function. E.g I have, letting ' and '' be the first and second derivatives,

m1x1'' = Fapplied - k2(x1-x2) - k1x1 - c1x1'
m2x2'' = k2(x1-x2) - k3x2 - c2x2'

So now I want to get X1/Fapplied and X2/Fapplied. I'm assuming I want two equations, F = f(x1(t)) and F = f(x2(t)) so I can do the Laplace etc. My first thought was to rearrange the second equation in terms of x1 and then sub into the first equation, but the algebra seemed pretty ridiculous. Is there an easier way? I have Nise but I don't understand the method it uses, it doesn't really explain how it goes from equations of motion to transfer function (or I don't understand the method it uses). Any help is appreciated.

 

[OldEngr63]

It sounds like you were on the right track but simply gave up because you did not want to do the algebra. There is definitely some algebra involved, so go ahead and work it through. It may be easiest if you set this up as a system of two equations in two unknowns in matrix form. It will fall right out that way.