First Order Differential Equation Problem

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Homework Help Overview

The discussion revolves around a first-order differential equation problem related to the motion of a weight attached to a spring. The scenario involves a 14 lb weight that stretches the spring by 4 inches and is released from a position above the equilibrium point.

Discussion Character

  • Exploratory, Assumption checking

Approaches and Questions Raised

  • Participants are attempting to determine the spring constant (k) using Hooke's Law and are questioning the definition of equilibrium in this context. There are discussions about whether equilibrium refers to the unstretched position of the spring or the position when the weight is applied.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of equilibrium and its implications for the problem setup. Some guidance has been provided regarding the relationship between force, spring constant, and equilibrium position, but no consensus has been reached.

Contextual Notes

There is some ambiguity regarding the definitions of equilibrium and the variables involved in Hooke's Law, which may affect the understanding of the problem. Participants are also navigating the constraints of the problem as posed in a homework context.

th3plan
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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
 
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First, this is a undamped second order problem.

I would consider equilibrium is when mg=kx.


th3plan said:

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

th3plan said:
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 ?
 

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