Figure 1 shows the raw data of the mass and the time trials for 5 oscillations.
Figure 1
The original brass weight with mass of 0.05kg, has the uncertainty of . With the addition of each weight after the original, the mass was applied to the mass uncertainty to create a new total uncertainty for the specific mass. Given below in the example calculations are the average time for five oscillations and the uncertainty for the original time measurements.
Example Calculations:
Finding Average Time for five oscillations
s
Finding Uncertainty of Original time measurements
3.47s, 3.34s, 3.53s, 3.41s, 3.69s and Average (3.48s)
Using:
Maximum Value – Minimum Value
And
Average Value – Minimum Value
Depending on whether which is greater, that will be the value used for the uncertainty.
Respectively
3.69 – 3.34 = 0.35
3.48 – 3.34 = 0.14
0.35 > 0.14
Hence, resulting in the uncertainty of ±0.35
Processing Data
With the current data retrieved from the experiment, we are not able to portray a graph that will accurately represent or depict the effect of mass for the time taken for one oscillation. The data must be processed to provide graphs that will accurately represent the effect of mass on the spring. Seen in Figure 2 is the processed data that will be graphed.
Example Calculations
Finding the Time Period for 1 Oscillation
Uncertainty for Time Period2:
Graphing of Processed Data:
Below, is Graph1.1 which portrays the connection of Mass (kg) and Period (s). As it can be seen, the graph shown is clearly not linear, but takes a more of an exponential curve shape. To linearize the graph the y value, Time Period, given by the term T, must be squared.
Graph 1.1: Showing the Relationship Between Mass and Time Period
Within
Graph1.2, the relationship between the Time Period2 (s) against Mass (s) is shown. Each of the graph’s gradients have been identified within the top left hand corner, though the uncertainty will be calculated in the Example calculation further down.
When compared to the previous graph, Graph 2.1 is far more linear which supported the theory previously stated, thus indicating that when the Mass values and the Time Period2 are proportional. However, when analysing the graph it can be seen that the y intercept is not equivalent to 0, thus suggesting the occurrence of systematic error.
Example Calculation:
Conclusion
Stated previously in Graph 2.2, the gradient of the graph is, as well as Mass of the brass weights and Time Period2 being proportionate to each other. This can be given in the formula:
T = Time period (s), m = Mass (kg), k = Spring Constant (Nm-1)
However, the values of T and m within the above equation are not in proportion, thus the equation must be manipulated.
This equation now shows that and m are now proportionate, meaning that if the value of m changes, so will the value of the Time period2. Further rearranging of the formula will result in the spring constant.
Where
Evaluation
To be using the formula , the mass on the spring should both be in harmonic motion, however in reality there is dampening thus the equation can not be used. However, this equation was only used to find the spring constant of the object and to investigate the proportional values of Time Period2 and Mass. To do this the assumption made was that the spring undergoes Simple Harmonic Motion so that the equation will work.