Modeling a Damped Spring System with Differential Equations

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Homework Help Overview

The problem involves modeling a damped spring system using differential equations. A mass is attached to a spring, and the system is subjected to damping. The initial conditions and parameters for the spring and damping are provided, and the goal is to find the equation of motion.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • The original poster attempts to derive the equation of motion using the weight of the mass and the spring's extension. Some participants question the interpretation of weight versus mass and the definition of the damping constant. Others discuss the nature of damping forces and their relationship to motion.

Discussion Status

The discussion is ongoing, with participants exploring different interpretations of the parameters involved. There is a focus on clarifying the definitions and units related to the damping constant and the forces acting on the system. Initial conditions have been noted, but no consensus has been reached on the correctness of the original poster's setup.

Contextual Notes

Participants are addressing potential misunderstandings regarding the distinction between weight and mass, as well as the implications of the damping constant provided in the problem. There is also a mention of the initial conditions that the original poster has set.

joker2014
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Homework Statement



After a mass weighing 8 pounds is attached to a 5-foot spring, the spring measures 6.6 feet. The entire system is placed in a medium that offers a damping constant of one. Find the equation of motion if the mass is initially released from a point 6 inches below the equilibrium point with a upward velocity of 1 ft/sec.

Homework Equations


F=kx
my''+cy'+ky=0

The Attempt at a Solution


I got k=8/(6.6-5) = 8/1.2
c= 1 as given ?

setting up the eqn I got 1/4 y'' + 1y' + 8/1.2 y = 0
or y'' +4y' + 80/3 y = 0

is this actually right? I tried 3 times and I keep getting this, i don't know i feel suspicious ?!
 
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"8 pounds" is weight, or force, not mass. What does "damping constant" mean? What are its units and how does it give force?
 
HallsofIvy said:
"8 pounds" is weight, or force, not mass. What does "damping constant" mean? What are its units and how does it give force?
of course 8 lbs is weight, dividing by 32 gives me .25 which is my mass! damping i believe is given in the problem "damping constant of one" .. otherwise if not given i would find it by sqrt of 4*m*k
 
"Damping force" is always opposite to the motion and is, approximately, proportional to the speed or the speed squared. I presume here you are told that it is proportional to speed. But because it is opposite to speed, the force must be -kv.
 
and of course my iniital conditions would be y(0)=-6 y'(0)=1
 

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