Understanding Parallel Springs & the Equal Extension Assumption"

[andyrk]

When springs in parallel are replaced by a new spring of a new effective spring constant, for the proof of this, i.e

k_eff=k₁+k₂​

Why do we assume the extension in the springs to be equal?

 

[Pythagorean]

If you imagine two adjacent blocks being held together by two springs, if you stretch the blocks apart, the springs stretch equally.

 

[andyrk]

In the attachment, why is the extension of the springs same?

 

[Pythagorean]

For the sake of the derivation, you assume that the little block is pulled evenly so that both springs are extended the same amount.