General relationship for springs connected in series

azizlwl

1. Let 2 bodies connected with inextensible string.
If 1st body is pulled by a force and remained at rest, EQUAL force also exerted on 2nd object.

Thus spring#1 and spring#2 extended with equal force, x1 and x2

F=-k1x1=-k2x2 .....(1)

2. Total extension is x1+x2 due to F.
F=Keff(x1+x2)

Subt. (1) in (2)
-k2x2=-Keff((k2/k1)x2+x2)
k2=Keff((k2/k1)+1)

Keff =k1k2/k1+k2 like resistors in parallel

ehild

You mean that Keff=k1k2/k1+k2, that is Keff=2k2? It is wrong.
Or you just forgot the parentheses...

ehild