Question #42367

This question tests the application of Energy Conservation in a non-linear conservative force field.

A common trap is attempting to find the work done by integrating the torque ($\int \tau d\theta$) while incorrectly assuming a constant moment arm ($L$).

This leads to an unsolvable elliptic integral $\int kL^2(\sqrt{5-4\cos\theta} - 1) d\theta$.

The correct moment arm is highly non-linear ($l_{\perp} = \frac{2L\sin\theta}{\sqrt{5-4\cos\theta}}$).

Recognizing that the spring force is conservative allows bypassing this complex integration entirely via the Work-Energy Theorem, separating rote formula application from physical insight.