# Springs in Series or Parallel

#### posto002

Homework Statement
You are given four springs, each with a spring constant k. What arrangements using all
four springs will result in an equivalent spring constant of k?
(a) All four springs in series.
(b) All four springs in parallel.
(c) Three springs in parallel which are then connected in series with the fourth spring.
(d) Two springs in parallel then connected in series with the other two springs which themselves
are in parallel.
(e) No arrangement of the four springs will result in an equivalent spring constant of k
Homework Equations
Hooke's law
I know that in parallel springs, x (the displacement of the spring) is the same for both springs. However, the forces resulting for each string are different. For springs in a series, x may be different, but the force is the same on each string. I got the answer b, seeing how the weight would be evenly distributed between the four springs. A simple 'yes' or 'no' on whether I answered the question right will suffice. Thank you for any help!

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#### haruspex

Homework Helper
Gold Member
2018 Award
Homework Statement: You are given four springs, each with a spring constant k. What arrangements using all
four springs will result in an equivalent spring constant of k?
(a) All four springs in series.
(b) All four springs in parallel.
(c) Three springs in parallel which are then connected in series with the fourth spring.
(d) Two springs in parallel then connected in series with the other two springs which themselves
are in parallel.
(e) No arrangement of the four springs will result in an equivalent spring constant of k
Homework Equations: Hooke's law

I know that in parallel springs, x (the displacement of the spring) is the same for both springs. However, the forces resulting for each string are different. For springs in a series, x may be different, but the force is the same on each string. I got the answer b, seeing how the weight would be evenly distributed between the four springs. A simple 'yes' or 'no' on whether I answered the question right will suffice. Thank you for any help!
Do the algebra. If one spring is displaced by x, what is the displacement of the others? What net force will result?

#### posto002

Oh! Right, thank you! That completely went over my head!

#### Delta2

Homework Helper
Gold Member
No b) is not the correct answer.

You can find the correct answer if you know that when two springs are connected in parallel, then the equivalent total $k_{eq}$ is $k_{eq}=k_1+k_2$ while if they are connected in series then the equivalent $k_{eq}$ is $\frac{1}{k_{eq}}=\frac{1}{k_1}+\frac{1}{k_2}$.

Using these basic equations you can calculate the $K_{eq}$ for each of the configurations (a) to (d) and see which turns out to be equal to just $k$.

"Springs in Series or Parallel"

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