I am having a hard time figuring out how to calculate the velocity of a mass in a spring-mass system with respect to distance, where the spring has a mass to it. The spring would be a long steel cable and a force of 4000 lbs would be applied to the system along the line of action. The cable is assumed to be long enough that it can be assumed to have a constant force. I have looked at it a couple different ways but not sure if it is correct. What I have come up with is: v=√(2*(F-Wc*Lc)*d/(m+(Mc*Lc))) where, v = velocity F = input force Wc = weight of cable/unit length Lc = length of cable retracted Mc = mass of cable/unit length d = equals distance m= mass of the mass (sorry that may be confusing) I was trying to add the cable weight and mass to the system as it contracts. Am I on the right track? Or am I way over complicating this and the mass and weight of the cable can assume to be negligible? I was starting to think I should use an integral to figure it out.