There is something physically I do not understand, consider this situation:
Lets assume there is no friction. if we defind $x_1$ and $x_2$ the displacement of mass $M_1$ and $M_2$ respectively, we get the equations of motion: $$ \begin{array}{l} M_1 \ddot{x}_{1}=-k x_{1}+k\left(x_{2}-x_{1}\right)=-2 k x_{1}+k x_{2} \\ M_2 \ddot{x}_{2}=-k x_{2}+k\left(x_{1}-x_{2}\right)=-2 k x_{2}+k x_{1} \end{array} $$
But I do not understand why for example when we look on mass $M_1$, where is the contribution of the most right spring?, if $x_1=x_2$ we get $$F_1=-kx_1$$ but $M_2$ got change it's location by $x_2$ so there must be force from the most right spring that should impact $M_1$ but according to equation of motion the only force is from the most left spring.