Velocity of spring mass system with spring mass

[Jwil]

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.

 

[Astrum]

I suspect the reason you haven't gotten any responses is because the questions is really confusing. Can you be explicit in exactly what you're asking?

Oh, and a tip, use the math script, it makes the math much easier to read, when you write it out in text, it makes it difficult to understand.

 

[Jwil]

After reading it again today I can see how it would be confusing. I am trying to find velocity of the mass that is connected to a really long spring that also has mass. The spring is initially stretched with some known force F. The mass is then released with initial velocity being zero. How would I find the velocity of the mass at a given distance from its initial starting point?

V=\sqrt{\frac{2*F*d}{m+Mc}}

I changed it from what I originally had because I realized I already factor in weight when I calculated the summation of forces at both ends. Also the spring and mass are oriented vertically and gravity is not neglected. Is that more clear or should I draw a picture?