An Investigation into what factors affect the period time of a simple pendulum

By doing an experiment I will investigate which factors effect the time period of each oscillation on a simple pendulum. This pendulum will consist of a mass hanging on a piece of string.In my investigation one oscillation consists of the complete to-and-fro motion starting from the centre. (See diagram).

Variables:* Length of pendulum* Mass of Bob* Shape of Bob* Angle at which the pendulum starts* Density of Bob* Gravitational field strength (constant on earth)* Material pendulum swings inDependent Variable:Time to make one oscillation (period (T))Preliminary Investigation:I have decided to investigate 3 different variables;1. Mass of bob2. Length of String3.

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Angle of AmplitudeResults:Mass of bobMassTime for 10 oscillations (secs)Period (secs)1512.751.282012.841.282513.061.

313012.811.283512.781.284012.961.30Length of String:Length (cm)10 oscillations (secs)Period2510.

311.0350141.47517.631.76100202Angle of Amplitude:Angle10 oscillations (secs)Period (secs)1012.81.282012.91.

293013.31.334013.51.355013.

71.376013.71.377014.21.

428014.31.439014.

81.48Analysis of preliminary results:From these results it is clear to see that the length of the pendulum is the only factor which has a substantial effect on the period of the pendulum. Both the angle of amplitude and the mass of the bob have little effect. Therefore, I will investigate how the length effects the period. There are a few things that I mist change from my preliminary investigation. I used an angle of 30� to drop the pendulum from, I found this too large and feel that it would give better and more accurate results to drop from a smaller angle such as 10�. The increments of the length of the string will be changed to 10cm and the range will be 10cm – 150cm, as this will give a much wider set of results. I will also repeat the results 3 times for accuracy.

Prediction:I predict that the period will be affected by the length of the pendulum. I predict that an increase in the length of the pendulum will produce an increase in time. I can say this because if the string is longer, it will have to travel a greater distance, so the time period will be longer.

When the pendulum is released its gravitational potential energy is converted into kinetic energy. The pendulum doesn’t lose its energy but just converts it over and over again until it is finally stopped by something such as air resistance and therefore energy is being transferred from the system.The longer the piece of string, the greater the gravitational potential energy will be. Therefore the velocity will be greater, if the velocity is greater this will in turn make the period bigger. I based my prediction on the scientific theory I found in a physics text book.From the research I have carried out I draw to the conclusion that I will investigate how the length of the pendulum affects the time period.

Equipment:* Clamp stand* Bob (45g)* String* Cork* Stop clock* Metre ruler* ProtractorMethod:- I will fix the string securely into the cork which will be held firmly in the clamp stand.- The clamp stand will be clamped to the table for safety reasons.- The metal bob which is a constant mass of 45g is attached to the string.- A protractor is fixed onto the clamp stand where the cork meets the clamp.

This will be used to keep constant the angle to ensure there is no variation of the forces acting on the pendulum. It will measure the angle at which the pendulum is dropped from. I have decided to drop the bob from 10� so to avoid violent swings of the pendulum.- When the pendulum is dropped from 10� I will observe the rhythm of the swing until it reaches the centre. I will then start the stop clock and wait for 10 oscillations to occur before stopping the clock and recording the period.

– I will do each length of string three times so I have three sets of results which I can find an average with and will make the experiment more accurate.- I will change the lengths of string with 10cm intervals. The range will be 10cm-150cm.- Once the results have been taken I will plot a graph showing length of pendulum against period.This method will work because there is only one independent variable which is the length of the string. The mass of the bob, the angle at which it will be dropped and the gravity will be constant. The method ensures that it is easy and relatively accurate to measure the period and therefore should come out with the correct results.

How to make the experiment fair:- The mass will be a constant weight of 45g.- The angle at which it will be dropped from will be a constant 10� ensuring there is no variation of the forces acting on the pendulum.- I will repeat each length 3 times to ensure accurate results and make sure there are no anomalies.- There will be a piece of card or some kind of indicator to show clearly where the centre is so I know when to start and stop the stop clock.- The length of string will change in 10cm intervals.- Ensure that the pendulum is not at all pushed but dropped from the exact height of 10�.

I think it may be a little bit hard to be completely accurate about when to start and stop the clock however the indicator will greatly help this problem. I think everything else will be very fair.How to make the experiment safe:- The angle of elevation will be 10� so there are no dangerous swings.- The Clamp stand will be securely attached to the table with a G-clamp so it does not fall over.- The pendulum will be checked to make sure it is tightly kept within the cork.- The cork will be checked to make sure it is tightly held by the clamp stand.

Diagram:AnalysisResultsLength of string (cm)Time for 10 oscillations #1 (secs)Time for 10 oscillations #2 (secs)Time for 10 oscillations #3 (secs)Average periodPeriod�106.66.76.60.660.44209.69.49.

30.940.883011.41111.21.121.254012.

712.712.81.271.615014.214.314.

31.432.046015.515.415.41.

542.377016.616.516.51.652.728017.817.

717.71.773.

13901919191.93.611002019.

820.12411021.121.321.32.134.5412022.

222.222.12.

224.931302323.223.12.315.

3414023.923.923.92.395.7115024.624.824.

82.476.1Conclusion:By reviewing my table of results and graphs I can find that my prediction was correct and I can find out the effect that the length of the pendulum has on the period. I have found out that the length of the pendulum has the most significant effect on the time period of each oscillation, as I predicted prior to the experiment.

By investigating this variable I found the pattern which determines the period. The period increases as the length does, but they are not directly proportional.The graph which shows period against length shows a curve which is at first very steep and then flattens out. This demonstrates that with smaller lengths of string the increase in period is more.

The graph showing period� is a straight line graph, meaning period� is directly proportional to length of the pendulum.From research I have found a formula which applies to the period of a simple pendulum;T = 2? Vl/gThis can be balanced out to show the formula for period�;T� = 4?� l/gl = length of pendulumT = Periodg = acceleration of free fallBy rearranging the formula again I have calculated the acceleration of free fall for 10cm;g = 4?� l/T�g = 4?� 10/0.44�g = 897.2367637Therefore, I can check that this formula works for my results by substituting the relevant figures;T = 2? Vl/gT = 2? V10/897T = 0.

66T� = 4?� 10/897T� = 0.44By referring back to my results I can see these are right.What has happened is that as the length of the string is increased the velocity has got bigger making the period bigger.EvaluateFrom looking at my results on the table, graphs and comparing them to the formula I concede that the investigation was successful.

I can apply the formula to my results and I got a straight line graph with period� against length and a curved graph for period against length, which from research I can tell is what is expected.My prediction was correct, as I had predicted the period to increase as the length of the pendulum increased, which happened.I can see that there were no anomalous results and as I did three sets of results and then found an average they were quite accurate. My results were accurate enough to draw a conclusion.

I found that when taking the results it was not entirely possible to get completely accurate results as there was not an easy way to recognize where to stop the clock, but it depended on your reaction times. I would prefer for there to be some indication of one oscillation if I were to repeat this investigation.My method gave me evidence that could be said to be reliable as it matches up with information I have found in physic textbooks about the formula and shape of graphs. I feel I had enough evidence as I had 3 sets of results for each measurement to find a average with as well as taking results from a large range (10cm – 150cm).

I felt it important to start measuring at 10cm because from 10cm until around 40cm there was a steep increase in time.