# Combination of springs

1. Oct 16, 2006

### emilykay

I dont understand how to calculate force constants of a combination of springs.

for example 2 spings parallel with the mass on one end lying on a table.

or 2 springs attached with mass at one end lying on a table.

i know that force constant = sum of forces/ extension
but just dont get how to combine springs!

Thanks!

EmilyKay

2. Oct 16, 2006

### rohit88

Hey Its Easy Man.just Assume The Springs As Resistance And Like We Calculate Net Resistances In Series And In Parallel Calculate The Net Spring Constant.ex-two Springs Of Spring Constant =k Conected In Series Are Equal Ti A Spring Of Constant 2k.the Masses Have Got No Role To Play.only Thing Is That U Have To Find How They Aye Joined In Seriesa Or Parallel.ok...

3. Oct 16, 2006

### tim_lou

when in Parallel configurations:
since they are parallel, the extension must be the same.
k=sum (F) / x
hence $$k=(F_1+F_2)/x = k_1+k_2$$

when in series configurations:
when in equilibrium, the tension in the two springs must be equal and the extension is the extension of the first spring + the extension of the second spring:
k=F/ (x1+x2)
take the inverse of both side:
$$\frac{1}{k}=\frac{x_1}{F}+\frac{x_2}{F}=\frac{1}{k_1}+\frac{1}{k_2}$$

4. Oct 16, 2006

### ZapperZ

Staff Emeritus
rohit88 response is incorrect. Please pay attention to the response given by tim_lou, which is the correct answer AND derivation.

Springs in series behave like resistors in parallel, which springs in parallel behave like resistors in series.

Zz.