# First Order Differential Equation Problem

1. Oct 21, 2008

### th3plan

1. The problem statement, all variables and given/known data
A 14 lb weight attached to the end of spring stretches it 4 in. Find the equation of motion if the weight is released from rest at a point 3 inches above equilibrium position

2. Relevant equations
F=kx
mx''+kx=0

3. The attempt at a solution

ok I need some help just finding out what the k constant is. I know I use hooks Law F=kx, and F is mg=kx. Do i consideer equilibrium when nothing is attached to it, and that is y=0? Then what is the x considered in Hooks Law equation mg=kx , is it the distant its stretched from equilibrium position ?

Thanks

2. Oct 21, 2008

### klondike

First, this is a undamped second order problem.

I would consider equilibrium is when mg=kx.

3. Oct 21, 2008

### th3plan

now what do u mean by equillibrium, is that when its unstretched and no wait? or the differecne between unstretrched and stretches in the middle in other words ?

4. Oct 21, 2008

### klondike

when the spring is stretched (downward) to x_0 such that kx_0=mg, it's equillibrium, that's y=0.