# Combining springs to match Force vs Extension Graph

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## Homework Equations

Hooke's Law: F = -kx
Series spring combinations: $\frac{1}{k_{eq}} = \frac{1}{k_1}+\frac{1}{k_2}$
Parallel spring combinations: $k_{eq} = k_1+k_2$

## The Attempt at a Solution

The slope of 1 is $\frac{4}{5}$ and the slope of 2 is $\frac{3}{2}$

I calculated that we would need $\frac{15}{8}$ times of the original spring to produce the same amount of force. Unfortunately that's just less than 2, so I can't just make it a parallel set of 2 springs.
So I know that in order to get a k of $\frac{3}{2}$ it must be a combination of both parallel and series springs.

So I set it up as such $\frac{3}{2} = \frac{1}{\frac{4}{5}} + \frac{1}{\text{some parallel combination of springs}}$

I get it so that it would be 5 parallel springs in series with a lone spring.
Does that logic sound correct? And the k_eff of the combination would just be $\frac{3}{2}$?

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haruspex
Homework Helper
Gold Member
the slope of 2 is $\frac{3}{2}$
Looks like a little more to me.

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