Mass-Spring Oscillations

Purpose

We had to calculate the period of a mass-spring system

Procedure

What we used:

• logger pro + motion sensor
• spring
• hanging mass(es)

What we did:

1.  first we had to calculate what the spring constant of our spring
2. then logger pro and the photo-gate were set up
3. the pivot is then placed at one of the locations (centered base or the top point) of the semicircle
4. the period is measured

Data

This is the data (right side) to help with finding the period vs spring constant 

 

Data Analysis / Calculations

We found the spring constant by measuring the height away from the motion sensor when the spring has a given hanging mass and the distance away with a different hanging mass. We then took the difference of the hanging masses and the displacement. We then found k through its relationship of F vs x. 

How we calculated for our spring constant

The expressions for what the period should be. Period vs Mass T = 1.678 m ^ 0.5 and Period vs Spring Constant T = 2.07 k ^ (-0.5)

This is the graph for the Period vs Mass. T = 1.971 m ^ (0.5556)

This is the graph for the Period vs Spring Constant. T = 2.132 k ^ (-0.4982)

Summary

In the lab, our results came close the calculated values. We calculated period vs mass T = 1.678 m ^ 0.5 and our experimental expression came out to be T = 1.971 m ^ (0.5556). For period vs spring constant we calculated T = 2.07 k ^ (-0.5) and in the experiment we got  T = 2.132 k ^ (-0.4982)
Our results came close to the calculated values that we can call the experiment a success.