Relationship Between K, Period, and Mass

Purpose:
The purpose of the experiment is to develop a tentative relationship between the spring constant, oscillating mass, and the period of oscillation of a spring. After the tentative relationship is found then a small discussion of where this relationship comes from will be held.

Equipment Used:

The set up is of a spring and hanging from it is a mass and there is a motion sensor to record position versus time. Three other groups each had a different spring but had the same "effective" mass on the spring to oscillate.
















Data Collected and Calculations:
First, the spring constant, k, of our group's spring needed to be calculated. This was done by hanging a mass and then recording how much the spring stretched. This was repeated twice more with more mass each time this was done and then the spring constant can be calculated.
Mass = .05kg, stretch of spring = .074m
Mass = .1kg, stretch of spring = .153m
Mass = .15kg, stretch of spring = .228m
Spring Constant of our group was 6.37N/m
Second, the relationship between the period of oscillation and the spring constant was compared. Four separate groups had different springs with different spring constants but the same effective mass was hung from the springs. The period of oscillation, T, were then compared to the spring constant, k.
k = 2.39N/m, T = 1.369s
k = 6.32N/m, T = .90s
k = 14.01N/m, T = .53s
k = 26N/m, T = .42s
From the data it is seen that as the spring constant increased, then the period of oscillation became smaller. Now that the relationship between spring constant and period of oscillation has been explored, the relationship between mass and the period of oscillation will be explored.
Mass = .105kg, T = .90s
Mass = .150kg, T = 1.033s
Mass = .200kg, T = 1.125s
Mass = .250kg, T = 1.25s
From the data it is seen that as the mass increases the period of oscillation increases as well.

Conclusion:
There were no predictions in this experiment but there should be an understanding of how the relationship between the two different variable affects the period of oscillation. From previous physics problems, the period of an oscillating mass is equal to 2pi divided by omega of the system. For a spring system, omega is the square root of the spring constant divided by the mass. So T = 2pi*(m/k)^1/2. So from the equation it should be predicted that as the mass increased, then the period of oscillation should increase but if the spring constant increases then the period should be smaller and that is what occurred in this experiment.

Sincerely,

Swaggy C