# Spring Displacement in Moving Part: Constant Pressure?

• Andrea Vironda
In summary, according to this scheme, you would calculate the acceleration of the center of mass (assuming it's not fixed) by multiplying the mass of the spring by the acceleration. Alternatively, you could imagine the spring as a chain of ideal massless springs connected via ideal pointlike masses, and use Newton's laws to calculate the acceleration of each mass.
Andrea Vironda
hello, I'm new here
according to this scheme:

i would to know, if the pressure is constant, the spring displacement in the moving part in function of time.
the square is without mass, so i thought to use the energy approach, but i don't know how to consider acceleration

If there is a force but no mass or an extremely small mass, what happens to acceleration? What does Newton's second law say?

The acceleration is Very high. But in this case The only mass i have is The spring, which is fixed on one extremity. I don't know how to consider this

Andrea Vironda said:
The only mass i have is The spring, which is fixed on one extremity.
The acceleration of the centre of mass times the mass is the net force.

Andrea Vironda said:
The acceleration is Very high. But in this case The only mass i have is The spring, which is fixed on one extremity. I don't know how to consider this
One way of considering it is to imagine the spring as a being a chain of ideal massless springs connected via ideal pointlike masses. As you apply force to one end of the spring, the masses near the force end move more and the masses near the fixed end move less.

In principle, you could use Newton's laws, write down an equation for the motion of each of the masses and solve them all.

If one imagines the limit of the process as the length of the component springs get shorter and shorter, the number of component springs get higher and higher and the masses get smaller and smaller, you end up with a continuous spring.

You can apply Newton's laws to obtain a differential equation defining the acceleration of each part of the spring in terms of the local mass density and the local tension gradient. With some simplifying assumptions you can solve this and obtain things like a wave equation.

[Or you could do as @A.T. suggests and imagine the spring as having its mass concentrated in the center. Way easier and probably accurate enough for your purposes].

A.T. said:
The acceleration of the centre of mass times the mass is the net force.
can i assume the spring free end acceleration as the double of the center of mass acceleration?

jbriggs444 said:
You can apply Newton's laws to obtain a differential equation defining the acceleration of each part of the spring in terms of the local mass density and the local tension gradient. With some simplifying assumptions you can solve this and obtain things like a wave equation.
i'm curious but I'm not able to implement this differential equation. can you give me a sketch?

Andrea Vironda said:
can i assume the spring free end acceleration as the double of the center of mass acceleration?
As an approximation, that ignores oscillation within the spring.

it's good, because i have to modelize a single-effect piston

A.T. said:
As an approximation, that ignores oscillation within the spring.
if i substitute i find i have ~1600g. i think this is the acceleration i receive if i cut the pressure supply outright.
if i have to calculate the acceleration the spring have during the room oil replenishment, how can i do? only for the forward stroke.

## 1. How does constant pressure affect spring displacement in a moving part?

Constant pressure does not have a direct effect on spring displacement in a moving part. The displacement of a spring in a moving part is primarily determined by the force applied to the spring and the stiffness of the spring itself.

## 2. What is the relationship between spring displacement and constant pressure?

The relationship between spring displacement and constant pressure is indirect. While constant pressure does not directly affect the displacement of a spring, it can indirectly impact the displacement by influencing the force applied to the spring. A higher constant pressure will result in a higher force, which can lead to a greater spring displacement.

## 3. How does temperature affect spring displacement in a moving part under constant pressure?

Temperature can have an impact on spring displacement in a moving part, even under constant pressure. Changes in temperature can cause the spring to expand or contract, which can alter its stiffness and therefore affect the displacement. This is why it is important to consider the temperature conditions when calculating spring displacement in a moving part.

## 4. Can spring displacement be controlled with constant pressure?

Spring displacement cannot be directly controlled with constant pressure alone. As mentioned earlier, the displacement of a spring is primarily determined by the applied force and the stiffness of the spring. However, by adjusting the constant pressure, the force applied to the spring can be altered, which can indirectly affect the displacement.

## 5. How can I calculate spring displacement in a moving part under constant pressure?

To calculate spring displacement in a moving part under constant pressure, you will need to know the force applied to the spring, the spring constant (stiffness), and the distance the spring will be displaced. You can use the formula F = kx, where F is the force, k is the spring constant, and x is the displacement. By rearranging the formula, you can solve for x and determine the spring displacement.

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