Lab 21

Goal:
This is the mass-spring oscillations lab and here we look to test the association between period of oscillation vs. mass, and period vs. spring constant. We will take data from different springs that have different spring constants and also take data for one spring with different masses. We will compare these data sets to see if our mathematical models of springs holds true.

Summary:
The whole class will work together for the first part of this lab, sharing data to facilitate speed. We start by measuring the period of 5 different springs oscillating with the same hanging weight. Josh came up with a method to easily match the hanging weight for all 5 springs. We measure the period of each spring. We also calculate the spring constant (k) of each spring. The second phase is to increase the hanging weight and observe the period. This gives us tables of data, one with constant mass but varying k, the other with constant k but varying mass. We graph these data points and use a power fit to model them. We should find that period (T) is proportional to mass and T is also proportional to k.

Procedure:
In order to measure the period of a spring we captured video of the spring oscillating and counted 10 oscillations and divided by 10 to find 1 period. We measured 10 oscillations from beginning frame to ending frame to in order to pursue an accurate measurement of period, considering this was our only data point of measurement. We incrementally increased our weight on our spring and measured the period to create our second data table. Lastly we input our data points into a logger pro graph and used a power fit curve to analyze their trend.

Analysis:
1.

2. We use a power fit to model the curve of our points because T is proportional to the square root of mass, and T is proportional to the square root of 1/k. Thus our power should be to 0.5 on both graphs. In addition, T vs k should be to a negative power. Our graphs match our assumptions.
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5. If k is off by 5% then T is off by sqrt(5).
6. The period should decrease if the spring constant increases. The reason is that a spring constant measures a spring's resistance to stretching. If a spring has a higher resistance to stretch, it will have a smaller period because it will "try" to return to its unstretched state more fervently.
7. Similar to how a spring constant is the spring's reluctance to stretch, the mass of an object is a measure of the objects reluctance to change its motion. Thus as the mass increases, it will take longer to complete a period of oscillation, thereby causing the period to grow as the mass grows.

Conclusion:
Our graphs accurately compare to our predictions, which makes us happy campers. In addition, I learned alot about the association between period, mass and spring constant in an oscillating system.