1. The problem statement, all variables and given/known data This is a required analysis for my Physics II lab. We recorded the motion of an object oscillating on spring, and are asked to use the slopes of different graphs that we plotted using the data collected in lab in order to find the spring constant (k). Both graphs were derived from the same data, which was amplitude of the objects motion, period of its motion, and maximum velocity of the object. We collected all of this information for a mass of 25 grams, then 30 grams, etc. all the way up to 75 grams. The first graph is a graph of Period^2 (s^2) vs. mass of object (kg). The line of best fit for this graph was f(x)=19.699x + 0.0652. In other words, f(x) should be Period^2, and x should represent mass of the object (s). The second graph is a graph of Vmax vs A/sqrt(m). The line of best fit for this graph was f(x) = 1.169x + 0.0396. In other words, f(x) should be Vmax, and x should represent the mass of the object. Both of the mentioned graphs should be linear. They were, and also had a R^2 value of .98 or higher each! 2. Relevant equations T = 2∏/ω = 2∏*sqrt(m/k) Vmax = Aω = A*sqrt(k/m) 3. The attempt at a solution We graphed T^2 vs m. So, using the relevant equation, we get: T^2 = 4∏^2 *m/k This means that if we graphed T^2 vs m, we should get Slope of graph (the derivative of T^2 with respect to m) = 4∏^2 / k Therefore k should = 4∏^2 / (slope of graph) ... right? If we plug in the slope that we obtained from our line of best fit, we get: k = 4∏^2 / 19.699 = 2.004 N/m The other graph was Vmax vs A/sqrt(m). Using the relevant equation, we get Vmax = A/sqrt(m) * sqrt(k) ... so, the slope of the graph should be the derivative of Vmax with respect to [A/sqrt(m)]. So... Slope of second graph (dVm/d(A/sqrt(m)) = sqrt(k) ...... right? So then, k = slope^2 If we plug in the slope that we obtained from our line of best fit, we get: k=1.169^2 = 1.367N/m. Note that 2.004 does NOT agree with 1.367! Why do you guys think this is? Do you guys see a flaw in my reasoning? I would not be surprised at all, because it seems like my derivative techniques were questionable at best!