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.