# Trouble predicting position equation on spring/mass damped system

## Main Question or Discussion Point

I am analysing a system that consists of a simple damper. The construction starts with a long compression spring; a small mass compresses the spring, and when released, the spring pushes the mass forward, until it hits a column of fluid. The mass has a controlled thru geometry, which allows the fluid to pass through at a linear rate, until the spring reaches its full extension, and the system stops.

I am trying to come up with an equation for position, as a function of time. So far, my general approach has been to find the velocity of the mass as it hits the column of fluid; to do this, I did a basic energy conservation for the the spring-mass system, ie:

KE1 + PE1 = KE2 + PE2

Where PE1 is the spring completely compressed, KE1 is zero (at t=0), and PE2 and KE2 is the spring at distance "X," which is the location of the column of oil. From this, I am able to get a decent value for my velocity @ the time it hits the column of fluid, I think.

Finally, I have tried sticking this value in to a generic solution for the SDOF diff. eq., ie:

http://www.efunda.com/formulae/vibrations/sdof_free_damped.cfm

now using "v0" from above, x0=0, and attempting to calculate "x" at a certain point during the damped portion of the stroke. Unfortunately, my mass is very small, and my damping coefficient has been calculated experimentally to be quite high. As a result, I am getting a damping ratio in the hundreds, and it is throwing my calculation for a loop.

I'm curious if my general approach is not correct ? When I plug everything in, my predicted time is a small fraction of a second, while in practice, this damper takes a few seconds to close completely.