Significance of spring mass in SHM.

1. The problem statement, all variables and given/known data
So, we are considering a spring-mass system, in which the mass at the end of the spring, M, is comparable to the mass of the spring, m.
Using Newtons laws, I have to calculate, how significant the mass of the spring is.

2. Relevant equations
Mass at the end of the spring, M.
Mass of the spring, m.
Spring constant, k.
Newtons second law, and Hooke's law.

3. The attempt at a solution
Actually, I have tried quite lot different approaches, but they don't seem to give me anything useful.
My latest attempt was to take a differential piece of mass of the spring, and calculate it's acceleration, in hope of getting something which i could integrate, but it didn't seem to work out.

I was asked this question by a high school student, whom I have to help writing a larger assignment.
I solved this problem rather easily using Lagrangian mechanics, but this is not available to the student, so I have to do it with Newtonian mechanics, which doesn't seem too easy.

I really appreciate any help I can get.

 PhysOrg.com science news on PhysOrg.com >> 'Whodunnit' of Irish potato famine solved>> The mammoth's lament: Study shows how cosmic impact sparked devastating climate change>> Curiosity Mars rover drills second rock target
 Recognitions: Homework Help Welcome to PF. I would think if you know the length of the spring that you can calculate the kinetic energy along its length by integration on the basis of the velocities all along it's length. Then you can relate that to the kinetic energy of the attached mass at the end.

 Tags mechanics, shm, spring