I know that the equation $mx''+cx'+kx=f(t)$ is used for a normal mass spring system, but I don't know how to express the differential equation for a coupled mass spring system with damping. These are the values:
First spring: $c=1$ $k=3$
Second spring: $c=3$ $k=1$
(no mass are given, so $m=1$)
The system is without external force, but placed in vertical position so $f(t)=mg$
Do I sum the constants of both springs so I can use the equation $mx''+cx'+kx=f(t)$? Or do I solve the equations for separate and then sum the final result? Thanks for your help!