# Finding effective spring constants

## Homework Statement

a) Consider 2 springs, connected in series. If they have different spring constants k1 and k2 then what is the effective spring constant for the double spring system? Give a convincing argument for your formula. You may assume that the mass of the springs is negligible.

b) Now suppose that 2 springs are hanging in parallel. (Assume that they are connected to the same point on a stand and on a hanging weight, so that they both stretch by the same amount.) They both have the same unstretched length but different spring constants k1 and k2. What is the effective spring constant for this double spring system? Again, give a convincing argument.
Fig 4.15:

c) Now suppose that 3 springs are connected in series, with spring constants k1, k2 and k3. What is the effective spring constant in this case?

d) Compare your formula for springs in series and parallel to the formulas for electrical resistances in series and parallel.

THANK YOU

## Homework Equations

F = ks
ka <-- effective spring constant
k <-- spring constant

## The Attempt at a Solution

a) equation 1 - F=k1s1 = k2s2
equation 2 - F = ka( s1 + s2)
combined equation: ka = (k1k2)/(k1+k2)

not sure what to do for part b and c and kinda have an idea for part d

CWatters
Homework Helper
Gold Member
Hints:

b) each spring produces a different force (if the spring constants are different). Do you know how to add two forces to make one equivalent force?

d) How do you add resistors in parallel? Compare with your equation for springs in series.

for part b) would it be like this:

equation 1: Fnet = k1s + k2s
equation 2: F = kas
combined equation: ka = k1 + k2