23-Nov-2016: Lab 21 Mass-Spring Oscillations Lab

1. Title: Lab 21 Mass-Spring Oscillations Lab
    Name: Qiwen Ye (Sherry)
    Partners: Matt
    Date: 23-Nov-2016

2. Purpose
In this experiment, we were trying to find the factors that affect the period of an oscillation of a spring. Also, we determined the relationship between the spring constant of the spring, the mass attached the spring and the period of the system.

3. Theory
According to the equation of the period of oscillation:

We found that the period of the an object was relate to the mass of an object and the its spring constant. Therefore, we separated the lab into two parts.
Part 1 - Same mass, different spring constant
We collected the data of period for same mass, where we varied spring constant k. We used the same mass of the system and different spring constant to find the relationship between the spring constant and the period of the system. We used five different spring that they had different spring constant, and let the mass of the an object and spring be the same.
Part 2 - Same spring constant, different mass
We collected the data of period on one spring, where we varied mass of the system. We used the same spring and five different masses to find the relationship between the period and the mass of the system.

4. Procedure
For part 1, we did the same experiment by five different groups with five different springs. Here was the set up of our group:

Placed the spring as shown, let the mass of the spring system=115g because all fie different groups need to have the same mass of the spring system.
For the mass of the spring system could calculate in that way:

Then, we used Logger Pro to find the position without mass and find the position with mass 115 gram as shown:

For part 2, used the same set up, but this time we varied the hanging mass on one spring: 20g, 40g, 60g, 80g, and 100g. Also, used the graph of position vs. time from Logger Pro to find its period because the period was the time of an object to complete one oscillation. For the Logger Pro set up, used the motion sensor to detect the movement of the spring, and then used the graph of position vs. time to find its period. 

5. Measured Date

Par 1, first, weighted the spring, then calculated the hanging weight that we need to make the mass of the whole system equal to 115g. Here was the process how to find the hanging mass. Our hanging mass was 110g.

6. Calculated/Result

Part 1 - same m, different k.

For the spring constant, we measured the height of the spring without any hanging mass (only the weight of the spring) and measured the height of the spring with hanging mass 110g (mass of whole system was 115gram). Then, used that formula we could find the spring constant.

We did the same experiment with different springs by different groups, here was the data we got from the other groups. 

Part 2 - same k, different m

In this part, we determined the period of the system on one spring (spring constant=2.5N/m) by using the equation of the period of oscillation. 

First, used the motion sensor to record the movement of an hanging mass that we could get the graph of position vs. time. 

Then, used 10 times oscillation to find the period as shown:

For the theory value of period, we used the equation of the period of oscillation, here was the example how we calculated the theory value of period in 20g:

7. Explanation/Analysis

We determined the graph of  period vs. oscillating system mass, and period vs. spring constant by entered the data into Logger Pro to create those graph. 

1) period vs. oscillating system mass

The period increased while we increased the mass attached the spring because when the spring of mass getting bigger it need more time to go back to its equilibrium.

2) period vs. spring constant 

The period decreased while we increased the spring constant because the spring with big k need less time to go back to its equilibrium, and the spring with small k need more time to go back to its equilibrium. (assume both equilibrium was the same)

8. Conclusion

In this experiment, we studied the mass-spring system by finding the relationship between 

the period, the spring constant of the spring, and the hanging mass. While we increase the spring constant of the spring, the period will decrease. While we increase the mass attached the spring, the period will increase. In part 2, we calculated the theory value of the period and compared to the experimental value, the different percent is less than 2%. It means that our experiment is successful. The factors cause our value different may be the spring constant of the spring is not exactly correct, or the air assistance affect the mass-spring oscillation.