Static displacement of a spring

[Dustinsfl]

Homework Statement

How would I find the static displacement of a spring due to maximum applied force? I asking this for arbitrary equation say $m\ddot{x} + kx = F(t)$.

Homework Equations

Hooke's law

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?

 

[nasu]

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

 

[Dustinsfl]

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

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.

 

[Orodruin]

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

 

[Dustinsfl]

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

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.

 

[Orodruin]

How would I find the static displacement of a spring due to maximum applied force?

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.

 

[Dustinsfl]

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.

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

 

[Orodruin]

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 ...

 

[Dustinsfl]

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 ...

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.

 

[nasu]

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

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