Pendulum Experiment

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100A

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Physics

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Jan 9, 2024

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Estrada,Villacastin 1 Cindy Estrada, Nina Villacastin Professor Aqiqi PHYS 100AL 7 November 2023 Simple Pendulum Experiment Description of purpose The purpose of the simple pendulum experiment is to study the behavior of a pendulum and explore the fundamental concepts of physics, such as gravity, oscillation, and periodic motion. A simple pendulum consists of a mass attached to a string or rod of fixed length, swinging in a circular arc under the influence of gravity. Description of Methods The description of methods in a Simple Pendulum Experiment typically outlines the step-by-step procedure followed to conduct the experiment. Here's how you might describe the methods for a simple pendulum experiment. The materials we used are a pendulum bob (a small mass attached to a string or a rod), a string or rod of adjustable length, a stopwatch or timer, a protractor (to measure the angle of release, if applicable), a ruler or meter stick, a stable support structure (such as a clamp stand), a pen and paper for recording data. Conclusion, results We investigated the relationship between the length of a pendulum and its period of oscillation. Our results clearly demonstrate that the period of the pendulum is directly proportional to the square root of its length, as predicted by the theoretical formula, T = 2𝝅 𝐿 𝑔 where T represents the period, L is the length of the pendulum, and g is the acceleration due to gravity. This experiment reaffirms the principles of periodic motion and the influence of pendulum length on its oscillatory behavior. Discussion of result The results of the Simple Pendulum Experiment unequivocally support the fundamental relationship between pendulum length and its period of oscillation. The experiment's data, when graphed, displayed a consistent and predictable pattern, confirming the expected linear relationship between the length ( L ) and the period ( T ) of the pendulum. These findings not only deepen our understanding of pendulum motion but also emphasize the practical applications of this knowledge in fields such as timekeeping and mechanical engineering.
Estrada,Villacastin 2 DATA: Pendulum behavior with different lengths. member l t (total time 25) T (Period) 1a 10 cm 19.31 s 0.6 s² 1b 15 cm 22.51 s 0.81 s² 2a 20 cm 25.15 s 1.01 s² 2b 30 cm 29.98 s 1.44 s² 3a 45 cm 34. 94 s 1.95 s² 3b 60 cm 42. 48 s 2.89 s² Large Angle Exploration 1. l = 10 cm Total time for 10: t = 7.57 s Period: T L-ANG = 0.8 s² ANALYSIS: 1. Include your graph of l vs T 2 in your report.
Estrada,Villacastin 3 2. From the straight line fit of your graph record the slope and intercept along with their uncertainties. (make sure to include the units): Slope = 22.39 cm/s² σ slope = 1.198 cm/s² Inter = -2.462 cm/s² σ inter = 1.973 cm/s² 3. Your experimental value of g. R^2 x 1000 = 988.7 g exp = 988.7 σ g = 4. Percent error in g. % error = 0.9% Questions: 1.) What value should the intercept of the graph of l-vs-T be? Is your value consistent with this? The theoretical value of g is 981 cm/sec^2. Then, theoretical value of slope = = 24.85 𝑔 4𝛑 2 981 4𝝿 2 𝑐𝑚 𝑠𝑒𝑐 2 Our value is consistent with this. 2.) Is your data of l-vs-T^2 consistent with the relationship between the two variables, even if the specific values aren’t? In other words, is your graph of L-vs-T^2 consistent with a straight line? Yes, the data collected is consistent with the relationship and the graph of L−vs−T2 is a straight line as expected. Graph of L−vs−T2 should be a straight line with a positive slope. Ours is a straight positive slope.
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Estrada,Villacastin 4 3.) Compare the value of T LARGE with the period of your smallest pendulum. Does pulling the bob back to a larger angle lengthen or shorten the period? By what percentage? The period of smallest pendulum is Tsmall=0.6 sec where length is 25 cm and angle of deflection is small. When we pull the bob to a larger angle for the same pendulum ( 25 cm ) ,the observed period is T LARGE = 0.8sec . Pulling the bob back to a larger angle lengthen the period slightly percentage change x 100 = 33% . Ideally, there 0.8−0.6 0.6 should not be any difference between the period for smaller and larger angles but there are few practical issues which cause a small change. This can mean more air resistance is experienced by the bob during a large angle swing and there may be some slack in the string momentarily when bob is released from a larger angle. Participation screenshots:

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