Symmetric Matrix Conditions for a Spring-Mass System

[MysticalSwan]

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.

 

[AlephZero]

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