Lab 1 Finding a Relationship Between Mass and The Period for The Inertial Balance

Purpose: To find a relationship between the mass placed in the tray of an inertial balance and the period of the oscillation of the tray, of the inertial balance. Once a relationship is found, using known masses, unknown masses will be used and the mass also recorded using a laboratory balance. The agreement of these variables will determine the validity of the relationship.

An inertial balance was clamped to a lab table. The other end was left free to oscillate with a small piece of masking tape used as a flag to break the beam of a photogate that will be used to measure the period of the inertial balance.

The Pendulum Timer experiment provided in Logger Pro was used to determine the period of the inertial balance.

The experiment was run with weights in the tray varying from 0g to 800g in 100g increments. The period was measured over many oscillations to increase the accuracy of the measurement. This data was then used to calculate the model using the following formula, provided in the lab manual.

\begin{equation}
T = A(m+M_{tray})^n
\end{equation}

The period of the inertial pendulum was plotted against the mass.

The graph was linearized by using the following formula, provided in the lab manual.

\begin{equation}
\ln(T) = n \ln(m+M_{tray})+\ln(A)
\end{equation}

The mass of the tray, Mtray, was varied to obtain the greatest possible fit value. This was then varied over the range that maintained the fit value. 

These values were then used to confirm the model for the inertial pendulum using the period and mass of a cell phone and 3 wooden blocks.