# A spring question

#### jacobsmith

I am rather confused about springs. This may be an obvious question, so just bear with me.

Now, say you had two spheres of any mass, a spring (that obeys Hooke's Law) connecting them, and the whole system was without external forces or friction (we can say, suspended in space). Now, what would happen if you applied a force to one of the spheres, in the direction of the other sphere? How far would the spring contract - would it even contract in the first place?

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#### stewartcs

would it even contract in the first place?
No. If there is no opposing force the spring won't compress. There must be a reaction force on the opposite end of the spring for it to compress. Otherwise, it will just move in space.

CS

#### nealh149

I disagree. Lets say we have two masses attached to a spring, m1 and m2. The spring constant is known and is equal to k. Let's say we push the masses with force F until the entire system is accelerating at a. We know, from free-body diagrams, that F-Fspring = m1*a and Fspring = m2*a. Eliminating a, we have (F - Fspring)/m1 = Fspring/m2. Solving for Fsrping we have (F*m2)/((m1+m2)) = Fspring = kx. Thus the spring will compress until x = (F*m2)/(k*(m1+m2))

#### russ_watters

Mentor
No. If there is no opposing force the spring won't compress. There must be a reaction force on the opposite end of the spring for it to compress. Otherwise, it will just move in space.

CS
The reaction force is due to the inertia of the spheres via f=ma. A force on one causes both to accelerate and a force between them (it'll be half the force applied to the first).

#### stewartcs

The reaction force is due to the inertia of the spheres via f=ma. A force on one causes both to accelerate and a force between them (it'll be half the force applied to the first).

CS

#### Topher925

You can decribe the response of the spheres with respect to each other with a simple second order DE.

mx'' - kx = 0

#### jacobsmith

You can decribe the response of the spheres with respect to each other with a simple second order DE.

mx'' - kx = 0
How would I apply this equation? Would I use it for both spheres?

And if I wanted to add in damping, the equation would be this: mx'' - cx' - kx = 0 where c is the damping coefficient?

Thank you all for your help.

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