20-Nov-2014: Oscillation Lab

Purpose: 

The purpose of this lab is for students to experience the relationship between the spring constant and the mass hanging on the spring. Also, to find the equation of the relationship with changing mass and changing spring constant.

Apparatus: 

With 4 different groups, each group gets a spring with different mass and spring constant. Each group has to have add mass to the spring up to .109kg before beginning the experiment. We hung our spring onto a rod that was clamped onto another rod which was clamped to the table. The motion detector should be right below the hanging mass which is hanging at the bottom of the spring. With Logger Pro set up, the data should collect the distance traveled, giving the amplitude of the spring. After collecting the data for the oscillation of the spring with the extra weight added on the hanging mass, we needed to do 3 more trials with different masses. This show give us 2 different graphs

Explanation: 

Our mass of the spring was 11.1g and the spring constant was 16.89N/m. The other spring masses and spring constant is shown in the picture below. Using these data, we graph period vs spring constant and come up with a power slope equation to predict a period for another spring constant. With the trials for different masses, we added 50g and 70g to the already hanging mass, so the total was 159g and 179g. To find the period, we used Newton’s 2^nd law to derive an expression for the period of the mass-spring system. The period for the original trial, with the hanging mass of 109g, was 0.814s. The period for the second trial, with the hanging mass of 159g, was 0.983s. The last trial, with the 179g, has a period of 1.734s. With these data, we should come up with a logarithmic curve to predict another trial with a different hanging mass. The equation for the graph Mass(M) vs Period (T) was 2.955*10^-4 x^1.651. The equation for the graph Spring Constant (K) vs Period (T) was 2.455 x^-.4309.

Mass (M) vs Period (T)

Spring Constant (k) vs Period (T)

Conclusion:

The class came up with the same graph for the Spring Constant (k) vs Period (T). The line was power fit and it gave that nice inverse slope. The Mass vs Period graph was our own, which came out not so well because we finished up our lab another day with another spring. This graph is misleading and not accurate.