Supporting spring, object, top spring problem.

[mechdesignron]

F_W+(Spring Force 2)K₂N₂(D₂-Delta)

(spring force 1)K₁N₁(D₁+Delta)

I have a spring set(springs in parallel) on top of an object and a spring set supporting the object. The weight of the object is represented by F_W. The bottom springs are F₁ and the top springs F₂. There is preload on the springs, represented by D₁ & D₂ repectively. I want to know how far the object will fall (Delta) in the given system.

I came up with this formula.

F_W+K₂N₂(D₂-delta)=K₁N₁(D₁+delta)

Some magic algebra and Presto:

delta=(F_W+K₂*N₂*D₂-K₁*N₁*D₁)/(K₁*N₁+K₂*N₂)

OK my problem. It doesn't seem to work. I plugged this into my handy-dandy spreadsheet and when I change the K value-keeping them both the same- it works fine. The higher the K the less the object falls. but when I change the compressed distance -keeping them both the same-, (which should, by hooks Law make the spring stiffer), does not change the distance the object moves. Please help.

Thank you

 

[Dr.D]

Clarify a couple of points, please.

What are N1 and N2?

What do you mean by "fall"?

What is delta?

How did you arrive at your equation? It might be a good idea if you would put your full development process in a post so that I can see how you got here.

 

[nvn]

mechdesignron: Assuming no coils touch, increasing the compressed distance of a linear elastic spring does not increase its stiffness. Instead, by Hooke's law, the force on the spring increases, not its stiffness.

I will call the spring constants of your two spring sets k1 and k2. Although you do not say what N1 and N2 are, we see from your formulation that k1 = K1*N1, and k2 = K2*N2. The equation in the middle of your post is correct. However, we know from equilibrium before Fw is added, k1*D1 = k2*D2. Substituting this into your middle equation, the equation simplifies to Fw - k2*delta = k1*delta. Solving for delta gives delta = Fw/(k1 + k2), which is exactly the result expected. In other words, no amount of preload compression (if your spring coils do not touch) changes the distance an added object drops (delta). The only way to change the distance the object drops is by changing k1, k2, and/or Fw. Your observed results are correct.

 

[mechdesignron]

Thank You nvn

It looks like nvn has awnsered my question but I will clarify to both clean up the post.
The top "equation" is an attempt at a free body diagram with the underline representing the supported object. N=number of springs, by fall I mean delta (the amount an object moves).