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)=[itex]\frac{x}{l}[/itex]V[itex]_{0}[/itex]


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[itex]_{0}[/itex] - 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([itex]\frac{L-z_{0}}{L}[/itex]))[itex]\ddot{Z}[/itex]=-[itex]\frac{L}{z_{0}}[/itex]k(Z-z[itex]_{0}[/itex])

if z[itex]_{0}[/itex] 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[itex]_{0}[/itex].
as you can see, this is probably not the right way to approach this question - way too complicated..

thanks, again.