Spring-Mass System Matrix

  1. The differential equation that model an undamped system of 3 masses and 4 springs with external forces acting on each of the three masses is

    m1x1''=-k1x1+k2(x2-x1)+u1(t)
    m2x1''=k2(x1-x2)+k3(x3-x2)+u2(t)
    m3x3''=k3(x2-x3)-k4x3+u3(t)​

    a)express the system using matrix notation x'=Kx+g(t) for the state vector x=(x1,x2,x3)T. Identify the matrix K and the input g(t).

    b) Give conditions m1, m2, m3, k1, k2, k3, k4 under which K is a symmetric matrix.




    I am pretty sure I have gotten the first part but I am having trouble even figuring out what the second part means. When I created my matrix K it seems like it is already a symmetric matrix. Any help would be great.
     
  2. jcsd
  3. AlephZero

    AlephZero 7,298
    Science Advisor
    Homework Helper

    I don't undestand part (b) either.

    The equations you are given will be symmetric for any values of the m's and k's - so what was the question really asking you about :confused:
     
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