Science Practical Report Title: Time Measurement Using Pendulum
Yi Jeong Hyun S3 Amber Tuesday 6 th September 2011 Aim: To calibrate a simple pendulum to measure time in seconds. - By differentiating the length of the string, figuring out how the length can affect the time of one period. - By differentiating the mass of pendulum, figuring out how the mass of pendulum can affect the time of one period.
Hypothesis: If I cut down the length of the string, then, the time of one period (of pendulum) will also decrease in a certain degree. I think the time taken will be reduced if the length of the string is cut down. I think like that because I used metronome in the music lesson in Korea. Metronome is a device that is used for measuring the time. If we reduce the length of the string, then, the movement becomes much faster than when it was longer. If I differentiate the mass of the pendulum, then, there will be no change I guess. It will keep the same speed. The reason why I think the speed will be the same is that when we see people playing on the swings, though the mass of each people is different, there is no much difference at the speed of each one.
Variables: - Independent variable: Length - Dependent variable: Time - Controlled variable: Mass of Pendulum
Apparatus: [ Rubber cork (the one that looks like cork), cork (made by wood), metre rule, retort stand and clamp, stopwatch, scissor, thread, balance ] ⅹ 1
Method: 1. Fasten the metre rule vertically to the retort stand by means of a clamp. 2. Tie the rubber cork to the clamp and measure the length of the string in metres. 3. Measure the time taken for the rubber cork to make 20 oscillations. 4. Vary the length of the string between 50cm to 5cm.
5. After the experiment is done, measure the mass of rubber cork and wood cork and figure out the difference of measure. 6. Tie the wood cork to the clamp and measure the length of the string in metres. 7. Measure the time taken for the rubber cork to make 20 oscillations. 8. Vary the length of the string between 50cm to 5cm. Warning: Do not forget to make the length of the string (wood cork) same as that of rubber cork. If not, we cannot figure out how the mass has effect on the time taken in one period.
Diagram: Results: Table: (the results of the T/s and T2/s2 will be presented into 2 decimal points.
Graph: Graph is attached at the back of this page (2 pages).
Data Analysis: As the length of the string increases, the period also increases. Also, for the graph of T2/s2 vs l/m, as the length of the string increases, the T2 also increases. However, the difference is that whereas the line is quite bended in the former graph, the graph of the later one is quite straight forward. It’s not bended. The period increased and increased as the time passed (both two graphs). The period was the longest when they length was the longest (0.445m). The period was the shortest when the length was the shortest (0.050m). For the former graph, the gradient was different every time. The gradient bent toward the x axis. However, for the later graph, the gradient was quite the same. They kept almost the same with small variation (no anomalous results). My line graph does not pass through the origin because we cannot measure the time when the length is 0m.
Discussion: My result has no anomalous results as I think it was the correct type of graph. I could clearly figure out the relationship between the independent variable and dependent variable. I think my method was very efficient as there are no steps that should be ejected or the steps that should be added. I think if someone follows my step and look at the diagram I mentioned above, they will be able to soon figure out how to do the experiment and can carry out the experiment. People can immediately carry out the experiment with the apparatus that I mentioned above. The apparatus can be easily found in the science lab. However, still, our method can be improved. First, we can say that it does not matter whether or not they do 20 oscillations. It was just our experiment. If they have more time, and they want their result to be more accurate, then, they can try 50 oscillations or 100 oscillations. Also, we can say that if they want, they can expand the length of the string up to the height of the retort stand. However, for those of people who want to carry out the experiment and make their data more clear to see the relationship between independent variable and dependent variable, I suggest them narrow the range between data points as I couldn’t. I hadn’t got enough time to do that as we had only 2 periods to do the experiment. If we can narrow the range between data points, we will be able to get more detailed result as we can minimize the error.
Conclusion/Evaluation: My hypothesis was correct as the mass of the pendulum didn’t really affect the time taken in one period and the length of the string had effect on the time taken in one period. When we see the graph of the rubber cork, the graph of T/s vs. l/m, then, we can easily figure out the period increases as the length of the string increases. The gradient shows that length has severe effect on the period. However, the fact is that, they do not increase linearly. The line is quite bended. The graph of wood, the graph of T/s vs. l/m also shows that when the length becomes shorter, the period also becomes shorter. Like the graph of the rubber cork, it is also quite banded. The line is bended toward the x-axis. When we see the graph of the rubber cork, the graph of T2/s2 vs. l/m, we can notice that the square of the period is directly proportional to the length. (The graph of the wood cork, the graph of T2/s2 vs. l/m also shows that the square of the period is directly proportional to the length.) Therefore, if we stretch out the straight line, we can easily predict the period of the pendulum for lengths that are not included in the graph we have plotted. (The length of the string affected the result greatly which can be shown by the result: as the string became short, the time taken also reduced. However, the mass of the pendulum and the force that I gave to the pendulum didn’t affect the time taken for one period. It can be explained about the Galileo’s research at 1602, which is: the period of the pendulum is approximately independent of the amplitude or width of the swing. Period is independent of the mass of the bob, and proportional to the square root of the length of the pendulum.) The step of pressing stopwatch affected my results. I had to press the stopwatch at when I start the experiment and when the pendulum finished 20 oscillations. Therefore, the result of mine is not 100% accurate as there are some times spent for pressing the button of the stopwatch. The behavior of rounding my results up also affected my results. I rounded up by two decimal points, so that people can easily notice what my result is. If I just let them have 6 or 8 decimal points, then, though it is more specific result of my experiment, it is quite hard to be drawn in the graph, and to read. Therefore, I rounded my result up so that people can be easily informed about the result of my experiment, though there are some errors. The other factor that may influence my result is the number of measuring the result. I did once unlike other students who did twice or three times. It may affect my result as I did only once and therefore, couldn’t divide the sum of two results by two, which is more accurate.
I chose the line graph to show my result as I think it is the best graph which can better show my result. When we use line graph, we can easily notice the relationship between dependent variable and independent variable. With any other graph like bar graph, we cannot easily notice the relationship as what we can show is just the bar. Without lining each highest point of the bars, we cannot easily figure out the exact relationship between those variables. (Though we can figure out which is the highest and lowest with bar graph, we cannot figure out the exact relationship with the bar graph. Bar graph is often used to show the lowest point and highest point of the graph and to compare certain number at certain period. Also, it is not often used to show the result related to time. Not only those reasons I mentioned above, but also the fact that the intervals of the length of the pendulum differs every time make the bar graph doesn’t really fit to show my result.) In the line graph, sometimes, the line is bended and sometimes the line is quite straightforward which shows what happens when we lengthen or shorten the time. To better figure out the relationship between independent variable and dependent variable, I think using line graph would be the best solution.
Limitations and improvements: Limitations Improvements
We just measured the time for 20 oscillations Next time, we can try measuring the time for which means the mistaken time is just more than 20 oscillations. It can be 50 or so. divided by 20.
We rounded our result up by two decimal Next time, we can try making our result more points which should have made my results accurate. We can try rounding our result up inaccurate. by three decimal points or more than that.
We did the experiment only once which Next time, we can try doing the experiment means that we couldn’t find the average. at least twice, so that we can get better result. Finding the average helps us to get more accurate result.
Basic information about the experiment: Pendulum: A pendulum is an object that is attached to a pivot point so it can swing without friction. This object is subject to a restoring force that will accelerate it toward an equilibrium position. When the pendulum is displaced from its place of rest, the restoring force will cause the pendulum to oscillate about the equilibrium position. In other words, a weight attached to a string swings back and forth. A basic example is the simple gravity pendulum or bob pendulum. This is a weight (or bob) on the end of a mass less string, which, when given an initial push, will swing back and forth under the influence of gravity over its central (lowest) point. The regular motion of pendulums can be used for time keeping, and pendulums are used to regulate pendulum clocks.
1602: Galileo's research: Italian scientist Galileo Galilei was the first to study the properties of pendulums, beginning around 1602. His biographer and student, Vincenzo Viviani, claimed his interest had been sparked around 1582 by the swinging motion of a chandelier in the Pisa cathedral. Galileo discovered the crucial property that makes pendulums useful as timekeepers, called isochronism; the period of the pendulum is approximately independent of the amplitude or width of the swing. He also found that the period is independent of the mass of the bob, and proportional to the square root of the length of the pendulum. He first employed freeswinging pendulums in simple timing applications, such as a metronome for musicians. A physician friend used it as a timer to take patients' pulse, the pulsilogium. In 1641 Galileo also conceived a design for a pendulum clock. The pendulum was the first harmonic oscillator used by man.
Bibliography:
Charlescammiso (2009). What is a pendulum. Retrieved from
WikiAnswers: http://wiki.answers.com/Q/What_is_a_pendulum on 8 September
2011
Drake, Stillman (2003). Galileo at Work: His scientific biography.
USA: Courier Dover. pp. 20-21.
Newton, Roger G (2004). Galileo’s Pendulum: From the Rhythm of Time to the Making of
Matter. US: Harvard University Press. pp. 52.