A simple pendulium is basically a inextensible length of wire at a fixed point, connected a mass called a bob. A period is a full oscilation, meaning when the bob has covered the distance from the point where it is released (A), to the point (E) the other side of the normal and back.In this experiment we will be investigating how the length affets the period of a pendulum.AimThe aim of this investigation is to see how length affects the period of a pendulumHypothesisi think that if the length is longer then the time of the period will increase, this is because, if the length of the wire increases then the wire will have to travel longer, because the radius of the circle increases, thus increasing the circumference of the circle, and therefore it would take longer to complete the period,, if compared to a wire with shorter length.Its the same as, if you were to travel around a longer cvircle then it will take you longer, then instead, going around a smaller circe.Apparatus1. Simple Pendulum x 5 (200cm)2. Bob3. Stand4. TimerMethod* I will set up the simple (shorter) pendulum on the stand* I will pull bob, backwards with my hands* I will release the bob from a angle of 45 Degrees. * Remember the angle of release has to always stay the same.* I will let it complete three periods, which will be timed with a stopwatch* Then i will calculate tge average for that length* Then i will repeat the experiment but with a longer length of thread. And repeat the experiment 6 x with 6 different length of wires.The length of the wire to be used in the experiment should be in this following order (15, 20, 25, 30, 35, 40, cm’s )DiagramVariablesIndependent: The length (l) of the thread. This is because, you have to it so that you cvan see weither the period will cahnge due to the length. i will manipulate the the variable by changing the length of the wire, so i will start with (l) 15cm and keep it increasing by 5 cm, so i will have 6 different length of wire and each alternative wire will have a difference of 5 cm from the pervious one. this will let me measure t, the changes caused in the period of the pendulum.Dependent: the dependent variable is the period of the osvialtion the pendeulum makes. This is because when the lenghth changes so does the periods. So basically the period is dependent on the length of the wire. to manipulate you will have increase the length of the wire.Controlled: The controlled variable si the height of the pendulum, the gravity, mass of the bob and the angle of release (45 Degrees).This is because you always ahve to keep these variables constant, as if you were to change the variables then the test would no longer be faith and the data would no longer be reliable.If you were to maniplualte the controlled then you change the degree at which you release the bob, so you could increases is by 10 degrees making it 55 degrees. Or you could change the high of the pendulum. But if you do change these variables then again your results wont be reliable no more.Or you would have to keep these changes constant through out the experiment, from the beginning.ResultsConclusionAs you can see from the results my hypothesis was right. If the length is greater than the the pendulum takes longer to complete a period. If you look at the 15 cm wire, you can see it takes 0.89 sec’ to complete a period. Where the 20 cm wire takes 0.99 sec’ and the 35cm wire takes 1.29 seconds. So you can see that the time increases as the length of the wire increases. This is because when the length is longer then the radius of the wire also increases, which makes the circumference of the circle bigger. When you have a bigger circumfernce, the pendulum has to travel longer to complete a period, but still has the same force of Gravity – 9.81 m/s. From the graph you can see that every 5 cm the period increase by a around about rate of 0.12seconds, and T^2 has a increase rate of 0.22 seconds; therefore we can conclude that T is proportional to sqrt (l), or that T^2 is proportional to the length. To check if the data above is reliable we have had to cross-check but using the formula for gravity: g = 4(pie)^2 x Gradient – gradient = l x T^2.If the formula give us 9.81 m/s this means that our data is very accurate, and the expermient is sucessfulGradient = l * T^2Gr = 35 / 1.66= 21.0843373G = 4 * (pi ^2) * GrG = 39.4784176 * 21.0843373G = 832.376273 cm / s=; 8.32 m / s. (2.d.p)8.32 m/s is very close to earths actual gravity, thus we can say that the data I got is very accurate and reliable. The gravity we got using the formula is not 100% correct due to some small errors, such as air, or the time when release, or the angle at release.If we were to get perfect results then we could conclude also that if L is proportional to time ^2 . Then we can say we should get a perfect line on the graph. Showing That 5cm is proportional to 0.2^2 secs.The experiment was sucessful as using the formula we can conclude. There were some errors in the experiement, one was the angle at which i released the bob – you see the point at which the bob should always be 45 degrees. But sometimes tho it was maybe one or two degrees off, maybe this wouldnt affect the results significantly, but it makes a difference. To improve next time i will take a very thin rod, and place at the point where the bob makes a angle of 45 degrees. Using a very thin rod, will allow me to reduce the error of being off from a few degrees, and i can place it agaist the rod, this will make sure its at the correct position while I release it.Another error was the timing of starting the stop watch as i released the bob. I wasnt always on time with the stop watch – the timing of it was not right. Next time i could use technology, so that i get the right timings, and the data is much more accurate. Or i could also tape the bob to the rod, and then using the scissor synchronize the stop watch and the releasation of the bob to be accuarte. It would work like this. The bob is taped, so i take a pair of scissors, and then i place the blade so that it can cut the tape and release the bob, while i place the handle of the scissors on the button of the stop watch that activates it. So as the scissors closes it cuts the tape, and comes nearer to the stop watch button. And when the scissor closes, it touches the stop watch button at the same time, as cutting the wire!Another problem that could have affected my results could be wind resistance acting upon the bob – it is insignficant but still . You would therefore have to do it in a wind free environment.One other problem was that, sometimes the bob wouldnt move straight, and wobble.To improve this you can, stretch the wire as furthest you can before you release it, and that should stop the wobbling, or otherwise take a bigger angle of release and again, stretch the wire as furthest you can before releasing it.

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