Error propagation for effective spring constant

[Tallah]

Homework Statement

Calculate the error propagation for the theoretical effective spring constant for the two springs. The actual values don't matter, it's just supposed to show how it would be calculated.

Homework Equations

ke=k1*k2/(k1+k2)

The Attempt at a Solution

ke=A*B/(A+B) (Let A=k1, B=k2)

I have come up with two possibilities, but I'm not sure if either is correct. The addition in the denominator is confusing me.

Possibility 1: σ(ke)/|ke|=σ(A)/|A| + σ(B)/|B| + σ(A) +σ(B)Possibility 2: σ(ke)/|ke|=σ(A)/|A| + σ(B)/|B| + (σ(A) +σ(B))/|A+B|

 

[anathema]

Solution:

it is important to accurately calculate error propagation in order to ensure the validity and reliability of our results. In this case, the error propagation for the theoretical effective spring constant can be calculated using the following equation:

σ(ke)/|ke| = σ(A)/|A| + σ(B)/|B| + σ(A)/|A+B| + σ(B)/|A+B|

This equation takes into account the errors in both k1 and k2, as well as the errors in their sum. This is because the effective spring constant is dependent on both individual spring constants and their sum.

Using this equation, we can determine the error propagation for the theoretical effective spring constant and ensure that our calculations are accurate and reliable.