T=A(m+Mtray)^n
We taped the end of the apparatus so the photogate sensor will read each oscillation. At the end of the device we add 100g weight for each trial. At each trial we slightly pulled the device so that it may sway back and forth until we felt comfortable to begin collecting data.
Here is one of our nine data collections we obtained during the experiment. At this moment we just started and had one 100g weight added to the device.
This graph (T vs M) shows the raw data being applied to a curve fit diagram. You can see our first record period with no mass was 0.286s. Each record we added 100g mass.
This graph (lnT vs ln(m+Mtray)) had the mass of the tray added into the expression. We also add several columns; total mass, ln T, and ln (m+Mtray). Then we received the curve fit equation. For our correlation to become 0.9999 we gave a mass of 250g to our tray. Which also ended up being our lowest guess for mass of tray. For our highest mass of tray we assumed 310g. In finding these masses we maintained our 0.9999 correlation.
From the slope we obtained our "n" value. With the y-intercept we were able to translate our "A" into e to the power of our y-intercept. Plugging in the period from our unknown mass we were able to calculate a range that the actual mass may be.
Given this experiment our group was able to plot points that gave us key values into using period as a means to obtaining information that was unknown to us. This helped understand the concept of deriving a power law for an inertial pendulum and the relationships involved. Though some errors may have interfered with a true value. For example, the placement of the masses during our nine trials, the clocking of the oscillations, how far the apparatus was pulled each time may have been different, old and used sensors, and other outside sources that may impact the experiment. Overall we manged to obtain the unknown mass using the period from our apparatus.
