$($This is an extension of an example given in class.$)$ Two particles, $1$ and $2,$ each of mass m$,$ are interconnected by a set of three springs, each with stiffness $k,$ and three dampers, each with damping coefficient c$,$ and slide on a smooth horizontal surface. A force acts on particle $2.$ Find the EOMs using $...$

a$.y_1$ and $y_2,$ where $y_1$ is measured positive to the right from a fixed reference point, $y_2$ is measured positive to the left from a fixed reference point, and where the springs are unstretched when $y_1=y_2=0.$

b$.$ Write the equations of motion from part a in matrix form. Are the mass, damping, and stiffness matrices symmetric?

c$.z_1$ and $z_2,$ where $z_1$ is measured positive to the right from a fixed reference point, $z_2$ is a relative coordinate that measures the stretch$/$compression of the middle spring $(z_2>0$ when the spring is stretched$),$ and where the springs are unstretched when $z_1=z_2=0.$

d$.$ Write the equations of motion from part c in matrix form. Are the mass, damping, and stiffness matrices symmetric?