First Order Differential Equation Problem

[th3plan]

Homework Statement

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

Homework Equations

F=kx
mx''+kx=0

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

 

[klondike]

First, this is a undamped second order problem.

I would consider equilibrium is when mg=kx.

Homework Statement

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

Homework Equations

F=kx
mx''+kx=0

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

 

[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 ?

 

[klondike]

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

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 ?