Linear velocity of a spring with mass

[tomerb]

Homework Statement

why does the velocity of an small spring element will be in linear proportion to the distance from the fixed end?

Homework Equations

v(x)=\frac{x}{l}V_{0}


Thank you very much,
Tomer

 

[tomerb]

I would like to add my attemp (although its probably way too far from the right direction):

the general force equation for any coordinate of a mass spring with mass M attached to it is (I think):
L - length of loose spring
z_{0} - the length from the fixed wall
Z - the coordinate of the small mass element.
m- mass of the spring
M - mass attached to the spring

(M+m(\frac{L-z_{0}}{L}))\ddot{Z}=-\frac{L}{z_{0}}k(Z-z_{0})

if z_{0} will be L then the equation will be the "normal" equation for mass M attached to a fixed spring.

from this differential equation I've got the general velocity depends on z_{0}.
as you can see, this is probably not the right way to approach this question - way too complicated..

thanks, again.