Oscillations with a Spring-Mass System

Purpose: The purpose of the lab was to see the relationship between oscillation and a mass-spring system.

Procedure: The whole data gathering was done by the class as a whole. We were divided into two separate sections. The experiment portion was done by groups individually. The equipment was set up as a previous lab with a stand and the spring with a mass at end oscillating above a motion sensor. In order to keep the experiment constant everyone had to have their mass-spring system weigh 109 g. The set up of the experiment is shown in the picture below.

The sensor was used to measure the spring constant like before and the period of the system. This information was shared with the class. Then we measured the period with four different masses. From all this information we could come to a conclusion whether the period and mass have a relationship. We also had the spring constant from the other groups from which we could find if the spring constant and period have a relationship as well.

Data: Most of the data that was taken was by Logger Pro.

The table below is the data that was shared by the entire class. The data that we took for our comparison was on the left side.

The table below was that of when we took the period of the mass-spring system.

The graph below was made from the data in the chart above. The graph will allow us to find the period of the 109 g system.

The table below was of the data we had gotten from the board.

The table below shows the spring constant for each spring and the period respectively. 

The graph below shows the graph from the table above.

The table below is that of the different masses we tried and their periods respectively.

The graph below was that of the mass vs. period.

Calculations: All the calculations done were to find the different relationships between period and mass or the spring constant and to find the period and spring constant.

The calculations below are for calculating the period and spring constant of the spring-mass system. 

Below are the calculations used to find the relationship between period and mass and period and the spring constant.

Summary: Overall the lab was a success because the period and mass as well as the period and spring constant were in direct correlation with each other. After finding the spring constant using the motion detector and the period using the oscillation pattern, we were able to come to a conclusion regarding the movement of the spring. Some errors that could have resulted would have been that the spring changes its moment of Inertia as it is stretched to its mass distribution changes.