25-Aug-2014: Deriving a power law for an inertial pendulum

The purpose of this lab was to find the correlation between the mass of an object and its period of oscillation.

 

Our apparatus contained three key instruments, an inertial balance with a piece of tape attached at the end, a photogate, and various masses. As the periods of oscillation increased the tape was substituted with a pen cap (as seen above) because the photogate failed to record any data.

The data recorded was taken from the amount of time it took the inertial balance to complete one oscillation with different amounts of mass. The masses of the various objects were also recorded in order to related the period with the amount of mass placed on the balance. By using this data and the equation given, T=A(m+Mtray)^n, we were able to construct a graph on logger pro that estimated the desired unknown variable that was wanted.

In this lab we conducted an experiment with involved the oscillation periods of various masses, including random items, and how the two relate to one another. To begin the experiment we set up a inertial beam that oscillations at different rates depending on its total mass. We tested numerous masses and objects and collected the data on the period of oscillation of the various masses. After collecting the data it was input into logger pro along with the given equation T=A(m+mtray)^n, and parameters which included the estimated masses of the tray. The data created a linear function, as it appeared to resemble, that gave an estimation of the slope of the graph, represented by variable n, and its y-intercept, represented by variable A. A mass of the tray's range was concluded and tested with the data of the random items chosen. Using the equation we determined the most accurate mass of the tray by plugging in the data previous recorded.