Velocity of spring mass system with spring mass

1. Aug 13, 2013

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.

2. Aug 13, 2013

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.

3. Aug 14, 2013

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?