I am currently working on a problem involving the spring-mass system below and its total length as a function of $k_1/k_2$. I have written out the equations for each of the masses, but I am not sure how to combine them into a matrix equation, or even if I did the equation correctly.
Starting from the left ($m_1$): $$m_1\ddot x_1 +k_1(x_1-x_2)+k_2(x_1-x_3)=0 $$
Next mass ($m_2$): $$m_2\ddot x_2+k_1(x_2-x_3)+k_2(x_2-x_4)+k_1(x_2-x_1)=0$$
$m_3$: $$m_3\ddot x_3+k_1(x_3-x_2)+k_1(x_3-x_4)+k_2(x_3-x_1)=0$$
$m_4$: $$m_4\ddot x_4+k_1(x_4-x_3)+k_2(x_4-x_2)=0$$
What is the matrix equation for the equilibrium position of the blocks?