Does it matter which direction the spring and damper forces point?
In one of the examples in my professor's lecture, he stated that if we define y to be positive when pointing up (see image below), then the damping and spring forces must be in the opposite direction. He went on with another example where he redefined the positive y axis to point downwards, and this resulted in the damping and spring forces to point upwards. Note: the gravitation force is missing in this picture.
I always thought that direction did not matter, am I right?
Best Answer
The direction matters. Consider this diagram:
This is using the up is positive convention, so the heights of the objects are positive, $y \gt 0$. A positive force is directed upwards so it accelerates the body upwards while a negative force is directed down so it accelerates the bodies downwards.
If you compare this to your diagram the spring is obviously pulling the body down, so the force due to the spring is negative.
The damper is a bit more complicated because the force due to the damper depends on velocity not position, so the damper force could be positive or negative depending on which way the body was moving..