24-Nov-2014: Mass-Spring Oscillations

Purpose:
The purpose of this lab was to find the relationship between mass and spring constant force in simple harmonic motion.

Apparatus:
The apparatus used in this experiment consisted of a suspended spring, a motion detector, as well as various masses which would be attached to the spring. Each lab group possessed a different spring, varying in mass and spring constant force.

Experiment:
Our first focus was to find the constant values of the spring we were assigned with, the values being mass and spring constant. The mass of the spring was found relatively easy with a scale. The value of the mass was recorded at 28.1 g. Next was the value for the spring constant which was found by measuring the distance the spring stretched when different masses were hung onto it. This was done using logger pro by find the equilibrium position when the spring was suspended with the 100 gram hook. As a result we recorded the average value of the spring constant as approximately 26.0 N/m.

Our next objective was to find the period of oscillation of our spring without any mass attached to it (only the 100 gram hook). Once again using logger pro we found that the period of oscillation was 0.42 seconds.

In order to do the second part of the experiment we needed other values for periods of oscillation and spring constants. This was done by comparing data with other groups in class.

Our final instructions were to construct two graphs, one for period vs time graph for our spring and the other for period vs. spring constant for a constant mass which would include the values from other groups.

The first graph required us to find the period of oscillation for three other mass in order to depict the change of the period with respect to amount of hanging mass.

After constructing the graphs above and finding the respective periods of oscillation the graph below was able to be generated.

The second graph merely required the data shared by the other groups.

Conclusion:
The graphs depict that a relationship exists between the mass of the spring, the spring constant, and its harmonic motion. As the mass increases so does the period of oscillation although being slightly. In terms of the spring constant, the greater its value the smaller the period of oscillation.This can also be proven with the equation for calculated period which states:

Period = 2(pi) (mass / spring constant)^(1/2)