# Spring Compression

1. Dec 11, 2004

### senseandsanity

How do you find the distance a spring is compressed by an object when kinetic friction is involved?

2. Dec 11, 2004

### dextercioby

Write Newton's second principle of dynamics in mathematical form including all the forces (they are only 2:the friction and the elastic force).To integrate the resulting ODE equation,your friction force must depend linearly on the speed (the example of viscous Stokes forces in fluids).From there,u'll find how the spring will oscilate.

The spring's compression understood as the amplitude of oscillation will decrease exponentially with time,so,eventually (for asymptotic times:t->+infinity),due to friction,the oscillations will stop and the body will stop as well.Where??That's impossible to tell,if u're in the "sin/cos" regime of oscillation.