The period of a pendulum Essays

The period of a pendulum Essays The period of a pendulum Paper The period of a pendulum Paper In this investigation, I will be looking at which factors affect the period (The time for one complete cycle, a left swing and a right swing) of a pendulum (a weight that dangles from a pivot so that it can swing freely). I will do this by tying a metal bob to a length of spring and dropping it from a certain height and measuring the time it takes to complete an oscillation, changing a variable for each of my preliminary investigations. Independent Variable Dependent Variable Control Variables Length of String (continuous) Period of the pendulum (continuous) Diameter of Bob Type of Bob Angle bob dropped from Person stopping stopwatch Person dropping bob Height Bob is dropped from Preliminary Investigations Preliminary One: Length of Strong Results Table Time of Period (seconds) Length of String Trial 1 Trial 2 Trial 3 Ranges Averages (mean) 10cm   68 According to my graph, there is a positive correlation between the period of a pendulum and the length of string, meaning that as the length of the string increases, the period increases as well. The gradient of this graph is 0.9879. This would be ideal for my main investigation as there is a noticeable relationship between the length of string and period. Preliminary Two: Angle Metal Bob is dropped from Independent Variable Dependent Variable Control Variables Angle from which the bob is dropped from(continuous) Period of the pendulum (continuous) Diameter of Bob Type of Bob Same person dropping bob Same person stopping stopwatch Height bob is dropped from Results Table Time of Period (seconds) Angle Bob is dropped from Trial 1 Trial 2 Trial 3 Trial 4 Ranges Averages (mean) 90i This graph clearly shows a negative correlation between the period of a pendulum and the angle from which the bob was dropped. This shows that as the angle decreases, the time it takes to complete one full oscillation increases. The gradient of this graph is 0. 8847. Although this can be considered for my main investigation, the gradient of this graph is shallower than the gradient of the first preliminary, meaning that my first preliminary is likely to give me more noticeable results than this preliminary. Preliminary Three: Diameter of Bob Independent Variable Dependent Variable Control Variables Diameter of Bob (continuous) Period of the Pendulum (continuous) Type of Bob Length of string Angle bob is dropped from Same person dropping bob Same person stopping stopwatch Height bob is dropped from Results Table Time of Period (seconds) Diameter of Bob Trial 1 Trial 2 Trial 3 Trial 4 Ranges Averages (mean) 13mm. 27 This graph also shows a positive correlation between variable and the period of the pendulum, meaning that as the diameter is increased, the time it takes the pendulum to complete one oscillation also increases. The gradient of the line of best fit on this graph is 1. This preliminary has yielded results that has a steeper gradient than my first preliminary, which means this is also ideal for my main investigation. Preliminary Four: Type of Bob Independent Variable Dependent Variable Control Variables Type of Bob (discontinuous). Period of the pendulum (continuous) Diameter of Bob Length of string Angle bob is dropped from Same person dropping bob Same person stopping the stopwatch Height Bob is dropped from Results Table Time of Period (seconds) Type of Bob Trial 1 Trial 2 Trial 3 Trial 4 Ranges Averages (mean) Iron 21 According to this graph, there is a positive correlation between the type of bob used and period. The gradient of this graph is 0. 9143. This gradient falls behind the Length of String and Diameter of Bob gradients, so its unlikely that I will use this for my main investigation, also, in terms of practicality, there wasnt a large variety of materials to choose from. Main Investigation: Length of String I decided to choose Length of String for my investigation, because, my results for that preliminary had the one of most noticeable relationships between the independent and the dependent variable as well as the fact that there were no outliers. I didnt choose Type of Bob, because Type of Bob is an example of a discrete independent variable, in that it doesnt have a numerical value that can be plotted on a graph. As well as this, even though there does appear to be a relationship between Type of Bob and the period, there was another independent variable which was changed, which was the mass of each bob. Although Diameter of Bob was also ideal to be tested in my main investigation, it lost out to Length of String simply because there was not a wide enough range of metal bobs that were made of the same material but had different diameter. So, although I predict it wouldve yielded noticeable results, Length of String is more practical to do, as well as the fact that the length of the string is easy to manipulate. Independent Variable Dependent Variable Control Variables Length of String (continuous) Period of the pendulum (continuous) Diameter of Bob Type of Bob Angle bob dropped from Person stopping stopwatch Person dropping bob Height Bob is dropped from Equipment Why Measure of Accuracy Nine different lengths of string To tie metal bob to and investigate Nearest centimetre Centimetres: Millimetres Clamp Stand To hold the pivot and the pendulum N/A. Metre stick To accurately measure out the correct lengths for the pieces of string Nearest millimetre Centimetres: Millimetres Scissors To cut the string as precisely as possible N/A Protractor To measure the angle from which the bob is to be dropped from Nearest degreei 19mm Iron bob The pendulum to swing from the pivot N/A Digital Stopwatch To accurately measure the amount of time the plant tissue soaks in the solutions for Hours:Minutes:Seconds:Milliseconds Method 1. Collect all required equipment. 2. Measure out each length of string to be used in the investigation, leaving an 8cm excess to allow for knot tying. 3. Tie bob to length of string to be tested securely 4. Set up clamp stand on the edge of the table to allow room for the pendulum 5. The person in charge of dropping the bob holds it up taut so that the bob is parallel to the clamp stand, or the length of string is perpendicular to the clamp stand and checks that the angle is 90i with the protractor. 6. Person in charge of the stopwatch signals when to drop the bob and measures the period with the stopwatch 7. Third person records results in a table 8. Retrial each length five times so as to that the results are as accurate as possible. Time of Period (seconds) Length of String Trial 1 Trial 2 Trial 3 Trial 4 Trial 5 Ranges Averages (mean) PE 10cm 01. 90 Results Pendulum Equation (PE): Time of Period=2? Interpretation: On the graph, there is positive correlation, according to my line of best fit. It appears as though the longer the string, the more time it takes for the bob to complete its oscillation. This can be explained because when the bob swings, it swings from a high position to its lowest position (the midpoint of the swing, also where the bob will come to rest when it reaches dynamic equilibrium). The change in height is caused by Earths gravitational acceleration or the change in velocity over time caused by gravity acting on the bob. If the length of the string is longer, the distance to swing from the highest point to lowest will be greater (as the distance travelled is the length of an arc, we can calculate the length of the arc using the equation 2? r x ? /360, where ? is the angle from which the bob was dropped from), therefore it would take a longer amount of time to fall to lowest point of the swing. Of course, gravity isnt the only factor that affects the period, other forces such as air resistance and friction help to eventually slow down the bob, and the mass of the string, although slight, affects the force needed to swing the pendulum back and forth. Evaluation The main investigation went well, however there are many areas which could be improved in order to get more accurate results. For example, the method wasnt very reliable because quite a few aspects of the investigation had to be carried out by humans, as well as the fact that the results which were recorded down were up to the judgement of the person who controlled the stopwatch when the bob completed its oscillation. This means that some of the results could be off by a few milliseconds or even seconds. Despite this, my group did try to keep the results as reliable as possible by making sure the same person was used to control the stopwatch and drop the bob, so that the factor of different peoples reaction times were limited. I could improve my experiment by:   Using a computer and a laser to release and measure the bob, for instance, if at its starting the point, the bob was intercepting a laser/beam of light, so that when it was dropped, the computer could measure the time it takes for the bob to re-intercept the beam again, i. e. complete its oscillation completely. Using a lighter sturdier form for the pendulum shaft instead of string, as the string had a tendency to bend throughout the oscillation, which couldve affected the results   Have a release that was positioned parallel to the clamp stand so that the angle from which the bob was dropped from each time was the same * Having a way to hook the pendulum length/string to the clamp and the bob without having to tie knots so the length of the string that would swing was more accurate Other than that, I believe my equipment was as accurate as I needed them to be, so I wouldnt change any of the equipment I was using to carry out the experiment. I think that my results are reliable because the range bars are all relatively small on my graph, however in comparison to the Pendulum Equation; the results are too big and are in turn not scientifically accurate. Ive calculated the average difference between my Averages and the Pendulum Equation line and have found it to be up to 0. 4 of a second in difference. In conclusion, I believe that the length of string does affect the period of a pendulum, despite the inaccuracy of my results as my investigation proved that this factor still theoretically affects it.