Modeling a Damped Spring System with Differential Equations

[joker2014]

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 ?!

 

[HallsofIvy]

"8 pounds" is weight, or force, not mass. What does "damping constant" mean? What are its units and how does it give force?

 

[joker2014]

"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

 

[HallsofIvy]

"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.

 

[joker2014]

and of course my iniital conditions would be y(0)=-6 y'(0)=1