For the motion in fig 4.1 (a), please check the description of this system in the images above, everything should be there. I get it, assuming the positive direction is downward, the spring tension is k(x-y), as (x-y) is the amount of extension by the spring. However, as the entire system is moving downwards (as the positive direction) and the base of the system is fixed to the ground, shouldn't the force of the damper point upwards (against the motion of the system)?
Therefore, I think the motion equation should be: $$ -cx(dot)+kx=ky $$ alternatively $$ -cx(dot)+k(x-y)=0 $$
By the way, I was viewing the motion at point A.Thus the tension of spring exerts a force downwards $(k(x-y))$. The damper exerts a force upwards $(-cx(dot))$.
Please help, as I am so confused at the moment.