29-Aug-2016: Finding a relationship between mass and period for a inertial balance

Apparatus: C-clamp, inertial balance, photogate, computer, and some masses.

Theory: Build a model of the relationship between mass and period and place the model in test.

Model: T=A(m+Mtray)^n

Process: We secure the inertial balance on the tabletop by using a C-clamp and then place a thin tape on the end of the inertial balance. We set up a photogate which can let the tape stay in the center of the photogate.

We set up the LabPro and use it to collect the datas. We place the 0g, 100g, 200g, 300g, 400g, 500g, 600g, 700g, and 800g mass separately on the inertial balance. Make sure that the period is reasonable by timing for some number of oscillations and comparing what you get with what the computer gets.
We record the period with no mass in the tray.

Using the LabPro makes a plot of  LnT  vs.  Ln(m+Mtray). And then we guess and adjust the value of the parameter Mtray until the graph gives us a straight line which means the correlation coefficient of 0.9998 to 0.9999.

We find out two values of  Mtray which make the correlation coefficient of 0.9998 and bound the actual number in a area. And then we find two equations of the relationship between mass and period accroding to calculation.

We find two other objects with unknown mass. We collect their periods, figure out their masses by our equation, and weight these two objects. And then we compare the datas to test our equation.