Static displacement of a spring

In summary, the static displacement of a spring due to maximum force is found by finding the maximal force and using Hooke's law.
  • #1
Dustinsfl
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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?
 
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  • #2
Do you have an actual problem in mind?
If it's "static" why do you have a time dependent force?
 
  • #3
nasu said:
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.
 
  • #4
If the force depends on t, then x is not static ...
 
  • #5
Orodruin said:
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.
 
  • #6
Dustinsfl said:
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.
 
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  • #7
Orodruin said:
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.
 
  • #8
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
Orodruin said:
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.
 
  • #10
Dustinsfl said:
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.
 

FAQ: Static displacement of a spring

What is static displacement of a spring?

Static displacement of a spring refers to the distance that a spring stretches or compresses when a force is applied to it and it reaches a state of equilibrium. It is a measure of how much the spring has deformed under the applied force.

How is the static displacement of a spring calculated?

The static displacement of a spring can be calculated using the formula: x = F/k, where x is the displacement, F is the applied force, and k is the spring constant. The spring constant is a measure of the stiffness of the spring and is unique to each spring.

What factors affect the static displacement of a spring?

The static displacement of a spring is affected by the applied force, the spring constant, and the length and material of the spring. Other factors that may affect the displacement include temperature, surface conditions, and any external constraints on the spring.

What is the significance of the static displacement of a spring?

The static displacement of a spring is an important measurement in understanding the behavior of a spring under a given force. It can be used to calculate the potential energy stored in the spring and to determine the maximum force that the spring can withstand before permanently deforming.

How can the static displacement of a spring be changed?

The static displacement of a spring can be changed by altering the applied force or by changing the spring constant. The displacement can also be affected by altering the length or material of the spring. Additionally, external factors such as temperature and surface conditions can also impact the displacement of a spring.

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