The range of the independent variable i.e. mass attached is 0.1kg – 0.6kg.
I am going to measure the dependent variable, the time period, using a stopwatch. Firstly, I will take 3 readings for the time of 10 oscillations for each mass added. Next, using the three readings, I will calculate the average time for 10 oscillations and divide it by 10 to get the time period i.e. the time for one complete oscillation.
I will finally plot a graph of T2 over mass to observe if the hypothesis I have stated of the relation between time period and mass attached to the spring stands true.
Regarding the controlled variables, I will be using the same spring throughout the experiment. Also, the clamp stand will be kept at the same position and the spring will be suspended from the clamp stand at the same height throughout the experiment. I will also make sure that I count the oscillations with regard to the mean pointer which I will place on the ruler.
I will repeat the experiment three times in order to get average time for 10 oscillations and then time period.
Method:
- Set up the clamp stand as shown in the picture above.
- Attach a ruler to the clamp stand and place the mean pointer on the ruler.
- Suspend the spring from the clamp stand as shown such that it is at a high point above the table.
- Add the masses to the spring one by one and oscillate the system to take reading of time for 10 oscillations.
- Repeat the experiment three times for each mass.
- Calculate average time by adding the three time trials for each mass and dividing it by 3. Then, calculate the time period by dividing the average for 10 oscillations by 10.
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Plot a graph between T2 and mass to verify the hypothesis.
Raw Data Table:
Processed Date Table:
Average time for 10 oscillations is calculated by adding the three time readings and dividing the result by 3 i.e. (T1 + T2 + T3) /3. The time period (t) i.e. time for 1 oscillation is calculated by dividing the average time for 10 oscillations by 10. The time period2 (t2) is calculated by squaring the time period.
The uncertainty for mass is smallest division on the weighing balance which is
± 0.01kg. The uncertainty for the each of the time for 10 oscillations is ±0.21. I took the reaction time test on Humanbenchmark.com. I found out that my average reaction time was 215 milliseconds which is 0.21 seconds. Since my values of time have an uncertainty during the experiment, my human reaction time is the uncertainty.
The uncertainty for average time is found by adding the general difference between the average time and each of the three readings and dividing it by the number of readings which in this case is 3.
The uncertainty for time period is calculated by subtracting the minimum time from the maximum time out of the three readings and dividing the result by 2. The uncertainty for time period2 is calculated by doubling the uncertainty for time period.
The uncertainty for mass is ± 0.01kg which is the smallest division in the weighing scale.
Source for reaction time:
Conclusion:
From the graph it can be concluded that the relationship between time squared and mass is a straight line passing through the origin which implies that mass is directly proportional to time square. Therefore, my hypothesis stands true. As we increase the mass attached to the spring, the time for one oscillation increases. The gradient in this case does not give any physical quantity and hence we need not find the uncertainty for the gradient.
Evaluation:
From the graph we can see that the results are fairly accurate as the line of best fit passes through all the points including the origin and hence there are no anomalous points. A considerable amount of error is expected to occur during the experiment and therefore the error bars which range from ± 0.02 to ± 0.04 appear to be realistic, not too big.
Causes of error
- The first and foremost is human error. Noting exactly when 10 oscillations complete is hard. This along with the reaction time in starting and stopping the stopwatch causes inaccuracies in the results.
- I did not measure the weight of each of the masses independently in order to confirm that they are 0.1kg each. The error bars for mass which is ± 0.01kg are too small to be visible on the graph.
- Yet another problem is that the spring does not always oscillate vertically. It often tends to swing back and forth and hence it becomes difficult to count the oscillations and take the time together.
In order to keep the controlled variables constant, I used the same spring to take all readings. The retort stand was kept in the same position and the spring was suspended at the same height throughout. The experiment was carried out in the same room to minimize the effects of air resistance.
The equipment used to calculate the time was a stopwatch which is not very accurate and hence the method used to carry out the experiment was also not up to full accuracy.
The experiment was not too long and hence time management was not a problem. The experiment was repeated 3 times in order to get more accurate results.
Improvements:
Although the results were fairly accurate, there are various causes which lead to inaccuracies. In order to eliminate the uncertainties in time I should use the electronic device called data logger which gives us more accurate results since there is no human reaction time. I can also try to oscillating the system slowly so that it does not swing in other directions and oscillates vertically. Also, I should measure the masses independently so that there are no uncertainties in masses.
I could have also repeated the experiment five times to get more accurate results and increased the range of the masses.
