Purpose:
The purpose of this lab is to find the relationship between a mass and its period using an inertial balance, which involves a power law equation that will show us the relation mathematically. We see how different masses and their respective periods behave on this device.
Process:
The inertial balance seen in the upper right hand of the paper, which will allow us to put masses on top of it and give us oscillations and a period of the mass.
The data that we took first was placing masses on top of the inertial balance. W started with 100 g, then proceeded to add more as we took the result for the period of each mass corresponding. We did this until we reached 800 grams, seeing 8 different results for the period and seeing a definite pattern. The period would increase as more mass was added to the inertial balance, which we then apply a force and see the resulting oscillations which we then cut off at a certain point to get the period. We also included two unknown masses.
We then proceeded to plot the equation T=A(m+Mtray) to the n power by taking the natural logarithm of each side and getting an equation very similar to the line equation y=mx+b. We must obtain the values of A, which is a constant, Mass of the tray and the exponent n. The graph would not be perfectly straight line, but to obtain Mtray we would need to try different values until we obtain a relative straight line. Then linear fitting it would give us the straight line we were looking for as shown above.
Conclusion:
Overall we plotted data with varying mass values, obtained the periods of each mass and saw that plotting the power law equation with the right values of Mtray gives us the desired line.
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