This lab concerns a mass spring system that displays simple harmonic motion, the goal of the lab is to find the period of the spring as a function of spring constant and the mass at the end of the spring.
In order to collect more data, we were one of 4 groups, each with a different spring with a different spring constant, each group would suspend the same amount of functional osculating mass, from the equation (M osc = M hanging + M spring/3)
Before we could measure period, we had to measure the spring constant of our spring. We treated it as an ideal spring that obeyed hookes law. So when the spring has a mass hanging on it and the system is in equilibrium:
Fnet=0=mg-kx
where x is the amount the spring stretches when the weight is added to the spring
mg=kx
k=mg/x
k=0.1(9.8)/0.067=14.64
What follows is our derivation of the theoretical relationship between period, spring constant, and mass
We then ran the experement 4 times with different hanging masses each time. The chart turned our as seen below
When our theoretical values were compared to our actual observed values for period, we found them to be extremely accurate. With this done, we turned to the other groups observations.
remembering that our theoretical T was calculated to be
T=2pi(m/k)^(1/2)
we predicted that
1. as m goes to infinity, T will go to infinity in a relationship T=m^(1/2)
2. as k goes to infinity, T will approach 0
To verify, we plotted the other groups periods against thier values for k and m. Giving us the following two graphs
As we can see, both our predictions played out. With T decreasing by a power law as k increases and increases by a power rule as M increases. There was a small amount of error between or predicted and observed values, but this is probably due to measuring errors or small inconsistencies in the springs used in the experiment.
You wanted T vs. oscillating mass, not T vs. spring mass. We don't have a prediction for that one. What you got doesn't match your prediction of m^0.5.
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