# Static displacement of a spring

1. Oct 8, 2014

### Dustinsfl

1. The problem statement, all variables and given/known data
How would I find the static displacement of a spring due to maximum applied force? I asking this for arbitrary equation say $m\ddot{x} + kx = F(t)$.

2. Relevant equations
Hooke's law

3. The attempt at a solution
I don't know how one would do this. Would it be find the maximum force and then use Hooke's law?

2. Oct 8, 2014

### nasu

Do you have an actual problem in mind?
If it's "static" why do you have a time dependent force?

3. Oct 8, 2014

### Dustinsfl

That is the type of equation of motion I have and the question is what is the static displacement due to the maximum force applied. I know $k$, $m$, and $F(t)$ but I looking for an explanation on how I would find this.

4. Oct 8, 2014

### Orodruin

Staff Emeritus
If the force depends on t, then x is not static ...

5. Oct 8, 2014

### Dustinsfl

This is a second question form the other question you answered. That is the exact verbiage of the question and you saw the problem statement and $x(t)$ solution.

6. Oct 8, 2014

### Orodruin

Staff Emeritus
I am pretty sure this is your interpretation of the problem due to how you phrased it, but it is not coming through so all I can offer is my interpretation of your interpretation, namely: What would be the static displacement if the force was constant and equal to the maximal value of F(t)?

Then yes, you would find the maximal value of F and plug it into Hooke's law due to force equilibrium at the static point. Alternatively, you would note that all time derivatives are zero for any static solution. Thus $\ddot x=0$ and you again get the same.

7. Oct 8, 2014

### Dustinsfl

I can take a picture of the question so you can see it is identical. I just added the how would I find.

8. Oct 8, 2014

### Orodruin

Staff Emeritus
In that case, the only interpretation I can find that makes any sense is the one above. Some problem writers really need to learn to formulate better ...

9. Oct 8, 2014

### Dustinsfl

One more question, $F_{\max} = \lvert F_{\max}\rvert$, correct? I think this must be the case since it is oscillating the max force could be in the reverse direction as well.

10. Oct 8, 2014

### nasu

Yes, this may be useful. Even if you reproduced verbatim part of the problem, you did not reproduce the text completely.