Independent variables:
 Length of string: For the string length, we took a wide range of 40140cm (every 10 cm) and therefore we did trials with 11 different string lengths. We used a meter ruler to measure the length of the string for each trial.
Dependent variables:
 Time taken for 20 oscillations: We measured these using stopwatches and took 3 readings for each string length.

Value of ‘g’: In reality, the value of ‘g’ is supposed to remain constant (approximately 9.81 m/s2). However, since our experiment is not perfect, the value of ‘g’ derived from our calculations might differ for each trial or string length.
Apparatus:
 Stand
 String
 Bob
 Meter rule
 Digital stopwatch
Diagram of Experiment
Digital stopwatch
Method of Collection of Data
 First set up the stand in an area which allows the pendulum to swing freely.
 Tie the string to the bob. Next measure the desired length of the string using a meter ruler. Make sure the length is measured from the center of the bob to the end of the string.
 Put the other end of the string between two rubber stoppers and clamp them tightly in the clamp in the stand.
 The experiment is now ready. Hold the bob at approximately amplitude of 15°.
 Once you let go of the bob, start the stopwatch and count for 20 oscillations.
 Take at least 3 readings for each length of the string to ensure more accurate data.
 Repeat for all 11 lengths
Data Collection and Processing
Raw Data
The uncertainty for the length is 0.05cm as the smallest unit on the meter was 0.1cm. Since the meter ruler is not a digital device, it is necessary to take half of the smallest unit to determine the uncertainty and so it is 0.05cm. As for the time, we used a digital stopwatch and smallest unit is 0.01s and so that becomes the uncertainty.
Processed Data
Now I will process the data and find the averages of the time. Averaging should reduce the uncertainty but I decided to keep the uncertainty same as before because of the variation in the uncertainty range for the different lengths.
T2 vs Length Graph
T2 (s)
Length (cm)
Note: Since the error is only 0.02s, the error bars are very hard to see on the graph but are still visible.
Value of ‘g’
In the graph above, the gradient is exactly 0.041118182. This was found using the trendline. Using this value we can find the value of ‘g’ using the formula I mentioned earlier.
Since the length was taken in centimeters, we have to convert the value to meters. This can be done by dividing it by a hundred.
Therefore my value of ‘g’ is 9.6 m/s2.
Conclusion and Evaluation
Conclusion
In my conclusion, I am going to relate what I got and what I was expected to get. My experiment investigated the relationship between length of string and time period and how to use that to find the value of ‘g’. As the length increased, the time period increased. This was clearly shown through my data table and graph. The actual value of ‘g’ was given as 9.81m/s2 however the value I got was 9.6m/s2. The percentage in my result would be {(9.819.6)/9.81} x 100 = 2.14%.
Despite doing the experiment to the best of my abilities, I still had a significant percentage error which could have been reduced. I came close to the actual value of ‘g’ and I am happy with my result. I believe that the experiment was a success and it also supports my hypothesis about the relation between the time taken and the length of the string. The reliability of my method was still good but it could have been improved vastly to ensure more accurate readings next time.
Evaluation
My experiment did contain some systematic and random errors. For systematic error, it could have been human error in which the amplitude of the bob was not kept constant and could have varied for each swing slightly. There is also the possibility that our reaction time to starting and stopping the stopwatch for each trial was different thus giving incorrect readings. As for the random error, we tried to reduce as much as possible by taking multiple readings so that we could spot an error if it was there. All of these combined would have had an effect on my experiment and thus giving me a slightly incorrect value of ‘g’.
There are many ways in which my experiment could have been improved. I could have constructed a better setup for the experiment which allowed me to keep the amplitude of the bob exactly the same for each trial. This could have been achieved through a clamp which holds onto and then releases the bob. To reduce human error, we could have used a light sensor which automatically starts recording the moment the bob crosses it and then stops recording after the bob has done 20 oscillations. This would give us a highly accurate reading for time as the reaction time of a human being is not being factored in.