How Do You Calculate the Effective Spring Constant k_eff for Springs in Series?

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SUMMARY

The effective spring constant \( k_{eff} \) for springs in series can be calculated using the formula \( \frac{1}{k_{eff}} = \frac{1}{k_1} + \frac{1}{k_2} \). This relationship establishes that the total extension of the spring system is the sum of the extensions of each individual spring, represented as \( F = k_{eff}(x_1 + x_2) \). The discussion emphasizes the importance of understanding the behavior of springs in series to derive the correct expression for \( k_{eff} \).

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  • Understanding of Hooke's Law and spring mechanics
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  • Basic algebra for manipulating equations
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ksmith159
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See attached file:
I would like to show theoretically that the first double spring system is equivalent to the second system with only one spring keff. Then I want to derive an expression for keff in terms of k1 and k2.

I think this system is in series and therefore keff =1/k1 +1/k2
but that is probably not even close to the right track...
 

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Well for the new spring system

F=k_{eff}(x_1+x_2)

knowing that F is the same for both springs, can you make an attempt now?

(sorry if I sound harsh,am a bit handicapped at the moment and typing is tedious)
 

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