# Linear velocity of a spring with mass

1. Dec 20, 2011

### tomerb

1. The problem statement, all variables and given/known data

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

2. Relevant equations

v(x)=$\frac{x}{l}$V$_{0}$

Thank you very much,
Tomer

2. Dec 21, 2011

### 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 - lenght of loose spring
z$_{0}$ - the lenght 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.