# Springs In Series

StephenPrivitera
Two springs are in series. You know the constants for each individual spring. How do you find the spring constant for the spring system?

|-OOOOO---o---OOOOOOOOOO-| --->F
In the middle of the spring system (where the "o" is) the net force is zero and we have
k1x1=k2x2 disregarding sign
F=k3x3
x3 =x2+x1
F=k3(x2+x1)
F=k3(k1x1/k2+x1)
F=k3*x1/k2*(k1+k2)
but F=k1x1+k2x2
F=2k1x1
2k1x1=k3*x1/k2*(k1+k2)
2k1k2=k3(k1+k2)
k3=2k1k2/(k1+k2)

Is this right?

heumpje
Looks OK.
Now try to find a similar expression for N springs..:)

Staff Emeritus
Gold Member
Looks to me like you have an extra factor of 2 in there. Springs in series add as Resistors in parallel. So

1/KT = 1/K1+ 1/K2

OR

KT= (K1+K2)/(K1K2)

Also Springs in parallel add as resistors in series.

KT=K1+K2

I do not have time to do the derivation now. Should be able to post it later to day. A key is that in the series case the force seen by each spring is equal, while in the parallel case the extensions are equal.

StephenPrivitera
Originally posted by Integral
Looks to me like you have an extra factor of 2 in there. Springs in series add as Resistors in parallel. So

1/KT = 1/K1+ 1/K2
Ah, I see my mistake. I have F=k1x1+k2x2 but F=k2x1=k1x1. I need to be more careful.

Staff Emeritus