Does Swapping Linear and Non-Linear Springs in Series Change System Behavior?

[user977784078]

Homework Statement

Suppose you have 2 springs in series, one is linear and one is non-linear. Initially the linear spring is at the top position and the non-linear is on bottom. Does swapping the springs affect the system?

Homework Equations

1/k_eq = 1/k1 + 1/k2
This equation doesn't apply though since we have a non-linear spring.
x_tot = x1 + x2

The Attempt at a Solution

I would say that it does not affect the system because x_tot in both cases will be equal, hence, F will be equal. x_tot = x1 + x2 = x2 + x1

Is this correct?

 

[BvU]

Dear user, welcome to PF :)

If you remember where the relevant equation came from, you see that there they added the extensions: x_total = x₁+ x₂ and substituted F/k₁ and F/k₂, respectively. So each of the springs feels the same F. That is also the case if the spring is not ideal and x is some other kind of function of F. So F isn't equal because the x_tot is equal (that is not a given; in fact that's what the exercise asks you to show!). But x_tot is equal because the F that cause the x_i is the same for each spring involved, threfore the x_i are equal, and yes, x₁ + x₂ = x₂ + x₁

 

[OldEngr63]

The same force acts through both springs (because they are in series). Each spring sees a particular deflection across that spring; the total deflection of the series pair is the sum of these deflections. The order in which the load gets to the spring is immaterial; they will experience the same relative deflections in either case. As BvU said (in different notation), d₁ + d₂ = d₂ + d₁

 

[user977784078]

Thank you. I understand now.

 

[HalfLostAndSearching]

Yes, your reasoning is correct. Swapping the springs in series will not affect the overall displacement or force in the system, as long as the total displacement is the same. This is because the displacement of the non-linear spring will be the same regardless of its position in the series, as it is not affected by the displacement of the linear spring.