After this review they proceeded to conduct a laboratory experiment. The primary task was to measure the potential energy stored in the spring system of the Partial Derivative Machine, however a process to determine this function was not explicitly given. The review of work, potential energy, and springs prior to data collection was designed to help students make the connection that the potential energy could be obtained from the work done on the system. Since the system was now two dimensional, using $W=\int \vec{F} \cdot d\vec{r}$ required finding the work done on the system in both the X and Y directions.

One possible solution method that determines all necessary information is:

1. Starting at a particular $x_1=x_{1,o}$, where $\Delta x_1=0$, take measurements of $x_2$ while changing $F_2$ in uniform steps, e.g., $0.05kg \times 9.81 m/s^2$.
2. Set subsequent $x_1$ values by loosening knob D, incrementing $F_1$ by small uniform steps, and then tightening knob D.
3. Repeat step 1 for each new fixed $x_1$ value.
4. Using the data and numerical integration of $F_1\, dx_1$ and $F_2\, dx_2$, approximate the value of $U(x_1,x_2)$.

This process gave students the data needed to get from any state $(x_{1,1},x_{2,1})$ to a different state $(x_{1,2},x_{2,2})$, provided each corresponded to a state generated during the steps outlined above. To verify path independence one would need to conduct a similar process, now measuring $x_1$ for fixed $x_2$ values while varying $F_1$ (changing $F_1$ and $F_2$ by the same increments used above). This lab also provided students practice distinguishing between fixed $x_2$ and fixed $F_2$ processes and the relevance of each to particular measurements.