# How can we prove that spring constant is always positive?

1. Jun 14, 2010

How can we prove that spring constant is always positive??

2. Jun 14, 2010

### Mapes

Imagine that you had a spring with a negative spring constant. If you hooked two of them up in series (with the other ends each attached to a wall, for example) what would happen?

3. Jun 14, 2010

### espen180

The sign of the spring constant depends on your definition of the spring force.

It may be $$\vec{F}=k\vec{x}$$, in which it is always negative, or

$$\vec{F}=-k\vec{x}$$, in which it is always positive (in these cases for ideal springs). The important part is that the spring force always tends to pull or push the spring back to equilibrium.

You cannot prove this. These force expressions are designed to fit experimental data. It is the same as trying to prove that like charges always repel. It just is that way.

Also, as Mapes pointed out, the opposite case leads to a runaway process when the spring is disturbed from (unstable) equilibrium.

4. Jun 14, 2010

Please give some experiment that can verify that K will always positive or always negative.

5. Jun 14, 2010

### espen180

If you have a spring available, you can easily confirm it yourself. In any case, I think that fact is incorporated in the definition of "a spring".

6. Jun 15, 2010