December 1 2014: Period of Oscillation

Purpose: To find the period of oscillation for two objects: a semi-circle and a triangle pivoted at different locations.

These two pictures show the apparatus that we used. First is a semicircle pivoted in the middle of the long side, we also did from the top of the curved side. Second is a triangle pivoted from one edge, we also did from the middle of one of the sides.

Explanation: First we are going to find the moment of inertia of each object pivoted at different locations by hand. From that we are going to calculate the period of the system from small oscillation angles. We are going to use two objects: a semi-circle and a triangle, and we are going to have two pivot points for each object.

 This picture shows the calculations to find the center of mass of the semi-circle, we found it to be 4R/3pi.

 This picture shows the calculations that we used to find the moment of inertia of the object pivoted at the two points. We got the long side to be 1/2MR^2, and the curved side to be 1/2MR^2+(1-24/9pi)MR^2.

This picture shows the calculations that we did in order to find the period of oscillation for each pivot point. From the long side we got 0.603s and from the curved side 0.59s

 This picture shows the period of oscillation for the long side by using LoggerPro. We found it to be 0.5994s.

This picture shows the period of oscillation for the curved side by using LoggerPro. We found it to be 0.5991s.

Here, we compared the results that we got by hand and by actually performing the experiment. The % error in both were less than 1%, which was the expected.

 This picture shows the calculations that we did to find the moment of inertia for the triangle at different points. We found it to be 1/24MB^2+1/2MH^2. The bottom part of the picture shows the period that we calculated when the pivot is at one end. We found it to be 0.77s.

This picture shows the moment of inertia when the triangle was pivoted at one of the sides. We found it to be MB^2/24+1/6MH^2. We also calculated the period of oscillation for this case to be 0.74s.

24 November 2014: Mass-Spring Oscillations

Purpose: To determine the relationship between the period of the system with the mass of the object and the constant of the spring.

This is the spring apparatus that we used for this lab experiment.

Explanation: First, each group will find important information such as period of spring with 109g (mass of spring + hanging mass) and constant of the spring by using a motion sensor and LoggerPro, then share the data containing the mass of the spring, mass add to the system, period of spring and spring constant. After that, we are going to calculate the period of our spring with 4 different masses and hopefully find a relationship between mass and period. Then we will use the constants of spring of each group and hopefully find a relationship between the constant of the spring and the period as well.

This picture shows the data collection of each group. The data that we used was from the left side.

 This is the data table that we got from LoggerPro when allowing the system to oscillate.

 This is the graph that we got from the oscillation of the system, we used this to find the period of our spring.

This picture shows the calculations that we did to find the period and the constant of our spring. The calculations are seen at the top of the page.

 This picture shows the data table that we used to find the graph of the constants of each group and the respective period.

 This is what the graph looked like from plugging the values for the constant (K) and period (T) of each group. We used this to compare our calculations made by hand with the real value.

 This is the data table that we used for graphing mass vs. period for our spring. We added different masses and calculated the period in order to create this graph.

This is what the graph mass vs. period looked like. We used this to compare our calculations with the real value.

This picture shows our calculations to find the relationship between the period and mass of hanging object, and relationship between period and constant of spring.

Summary: To conclude this lab, we can say that our results were pretty accurate. From the picture above we can see that for our estimated period with respect to mass was T=1.25m^0.5, and from the experiment we got 1.14m^0.4475, which is close to the calculation that we had. For the period with respect to constant, we calculated to be T=2.07k^-0.5, and from the experiment we got 2.66k^-0.5, which was a little off, but still considered to be close. We can say that our calculations were accurate enough if compared to the results coming from the actual experiment.