Those F's aren't the same as the one in "F = ma" though. The one in "F = ma" means "the (vector) sum of all forces on the object". You can write down, as you s

Those F's aren't the same as the one in "F = ma" though. The one in "F = ma" means "the (vector) sum of all forces on the object". You can write down, as you say, a bunch of contributions like F_spring and F_damp etc. that can be functions of other variables like x, v etc. "F = ma" then tells you that if you sum up all the forces (F_spring, F_damp etc) you have an expression for the acceleration. This gives you an equation of motion that you can solve to find out how the object will move given some initial state. Basically, if you know the initial position and velocity, you can compute acceleration at that time. Then you can figure out the position and velocity of the object a short time later, and recompute the acceleration using these new values. Then you can step forward again, and again, for as long as you want.