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.
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