11/23: Mass-Spring Oscillations

Title: Mass-Spring Oscillation
Purpose: The purpose of this lab is to find the relationship between period, mass, and spring constant.
Apparatus: We attached a spring with a known mass to a stand and attached various weights to the spring. The spring and the hook both have a mass, so they must be accounted for. 1/3 of the spring's mass as well as the mass of the hook must be added in addition to the hanging mass to make for the total mass.

Theory:

With this relationship, the period can be determined as long as the spring constant is constant and mass is varying.

Data:
The different periods of varying spring constants with mass constant

The different periods of varying masses with spring constant constant

Graphs/Calculations:
Calculation of spring constant

Calculation of hanging mass

Calculation of theoretical period (1 example)

Graph of Period vs Mass

Graph of Period vs Spring Constant

Analysis:
To determine the spring constant, we measured the initial position of the spring. We attached a mass to the spring, and then determined how far the spring was stretched. The relationship F=kx was used to determine the spring constant. In order for the mass to be correct, 1/3 of the mass of the spring as well as the mass of the hook had to be taken into account. The graphs show a very nice power fit curve. The period vs mass was slightly more accurate to the fit than the period vs spring constant. However, both correlations are very close to 1. When the mass increased, the period increased. This is because the heavier weight on the spring causes it to spring back slower. The heavier weight is harder to fight against the natural gravitational acceleration of the earth. When the spring constant increased, the period decreased. The "stiffness" of the spring causes it to have a shorter period.

Conclusion:
The percent error of all the trials are less than 1%, with the exception of the 115g, which was at a 1.2% error. This shows that the theoretical model is a valid equation for finding periods of oscillations. Sources of error may form from timing the oscillations, as the time at which we started and stopped the stopwatch as well as counting the oscillations may be off.