How do we calculate the effective spring constant of springs in parallel, where the springs have different spring constants and different stretch distances (because the original lengths of the springs are different).
Hooke's Law --> Fx = kx
The Attempt at a Solution
If we assume the stretch distance of both springs are equal (x), and each spring constant is k1 and k2 respectively. Then the effective spring constant of the springs in parallel is:
F = k1x + k2x = (k1+k2)x
From above, one can see that the effective spring constant is k1+k2. However, I assumed the distance would be equal, therefore I was able to common factor it.
So, now my problem is, what happens if the stretch distances are different. Then the above equation becomes:
F=k1x1 + k2x2
As one can see, I cannot common factor anything.
EDIT: I'm ultimately looking to find the effective spring constant and in this case, I cannot common factor, so I cannot find the effective spring constant.