Analysis of Oscillation of two coupled pendulums
The lab report indicates a physics experiment that explores fascinating behavior of pendulums particularly when they interact with each other. A pendulum is a body suspended from a fixed point so that it can swing back and forth under the influence of gravity. Two separate pendulums behave simple harmonic motion and have a definite demonstration of frequency. When the two oscillators or pendulums are attached to each other through a system then the system behaves differently compared to the previous harmony and the frequency. The lab report includes the abstract part, introduction part, theory part, experimental setup with apparatus part, result and discussion with conclusion part. The analysis of the lab report is not the proper indication how each step is taken but the analysis indicates how each part of the lab report makes a report fruitful and useful for a reader to understand the purpose of the report as well as the flow of the contents.
Abstract:
Analyzing the basics in the abstract, this is the starting and primary basis of a lab report where the basics are mentioned in a simple style also with basic introduction of the experiment what could have done in the test. The experiment aims to find normal modes of the frequency of the pendulum system. Two pendulums can influence each other’s motion greatly. There might also be multiple modes each with a distinct pattern. The time mentioned in the text refers to the time taken for a complete cycle of oscillation in that specific pattern. Analyzing the objective, it could be said that the experiment aims to observe the actual behavior of double pendulum and compare that with theoretical predictions. (1)
Introduction:
Introduction then comes after the abstract where the basics of pendulums and what could be come in the final results are discussed. A simple pendulum can oscillate at a certain frequency. If two pendulums are coupled together then the system would be more complex and behaves differently. Then the pendulums will not oscillate in a single frequency rather than it have normal frequencies at which it can exhibit periodic motion. During the experimental data, the introduction is more briefly analyzed how the normal modes of the system can be observed in that portion. Normal modes are periodic motions of a vibrating system where all parts of the system vibrate with each other in the same frequency. (2)
Experimental Setup:
During the experimental setup and apparatus, the figure was shown in the lab report how two pendulums were placed and how they acted in the determined position. Tension in different portions of distance denoted by d and l were addressed as t and T in the nomenclature. The two starting points of the lifting of pendulums with balls were denoted by p1 and p2 and the stands by p and p’. The extensible string was used for this setup. The ends of the strings were fixed using tapes for minimizing energy losses and effects of dumping. Pivot points meaning an indicator used to determine the trend of a place over different time frames were also set up to the string and not fixed as the distance needed to vary for the experiment. (3)
Theory:
The theory presents how some equations basically work together to represent an idea and context to work for a lab experiment. For this report, to make a statement, the theory could be said as a main part of the lab report how pendulum’s oscillation works. According to the experiment theorem, A common string connects the crucial points of these pendulums, creating a novel coupling mechanism. According to this setup, tension in the string is created whenever one pendulum moves, which transfers energy to the other pendulum. While operation of the separate pendulum, each pendulum shows single harmonic oscillation, but the combined setup design drastically changes how they move. Some equations can be solved to clarify the system’s oscillation modes and provide many notion patterns that connected pendulums can display. To further comprehend this complicated motion, two specific points of interest—p1 and p2—are chosen for examination. These locations probably act as focus points for watching and analyzing the pendulum dynamics. By using this methodical approach, the coupled pendulum system may be fully understood, revealing the complex interactions between its parts, and explaining their behavior. The indicated vector equations (forces acting point) represent tensions as being proportionate to the lengths of the strings, and the equations under consideration(with tangent) include vectors that represent forces operating either parallel or antiparallel to the length vectors. Furthermore, the selection of Point P, as shown in the corresponding figure, fulfills an essential function as the assigned origin or reference point. The analysis gains a frame of reference by choosing a certain point to serve as the reference, allowing for the measurement and comprehension of the motions and interactions of other system constituents. This calculated decision simplifies the analysis procedure allowing for more simplified behavior of the system. The situation and the setup explore the modes of oscillation with specific emphasis on their motion in y axis direction. The total of the y-components of the pendulums’ motions represents the first oscillation mode, or Q1. This mode corresponds to a certain frequency, wi, and is defined by the equation Qi = Ly + Izy. On the other hand, the difference in the ycomponents of the pendulum motions yield the second mode of oscillation, denoted as Q2. This mode corresponds to a unique frequency designated as w2 and is represented by the equation Q2 = Ly – Lzy. The passage clarifies that the y-direction is perpendicular to the plane of the page, which is important. Understanding the spatial direction of the pendulum motions under analysis requires this clarification. Cosine functions are used to depict the y-axis motion to clarify the motion given from the resulting equations. The second mode from 180 degree out of the first mode normalizes the frequency (shown in figure 2). The intricacy of the coupled pendulum gives in a normal result of two separate average modes. The procedures running in reverse continues and other pendulum will start losing amplitude until the previous one stops while transferring all energy back to the first one. From figure 3, the mixed oscillation represents a normal graph of oscillation of frequency where the maximum tends to Tp and the distance from amplitude to neutral is T. A relation can be built from the ratio of t and Tp where x is constant. If we substitute the value of other equations in the last, we get a relation of x through d and l measurement from the experiment. (4)
Results:
Two pendulums of equal length attached to a light extensible string recorded several measurements with an uncertainty of ±0.3 cm. The result was shown through a table with independent variable, d and dependent variables l and t with error percentage. The first table shows seven columns of d, lx, lz, T1, T2, T and Tp having parameters of cm and second. The recorded video was at the frequency of 30 fps. The second table showed xp and x1 and the percentage counted as difference of the value. It is the difference between the calculated value (xp) and value based on lengths measurement. The data shown suggests that the period of the pendulums is affected by the distance between them. Then in the later part of result showed a graph of those values from figure 4, the difference was analyzed with proper mention of the error percentage. (5)
Discussion:
The discussion part is the brief discussion of the result where the value with error is analyzed with logic and experimental values. The graph here shows a linear relationship between experimental values and the points that make the line of best fit. There is a 5% average difference between two values which means the good indication of a theory. The uncertainties during the experiment could be reduced by better equipment and the computed accurate measurements. A high-speed camera and the length controller also play a great role in the experiment which could make the experiment more realistic. Overall, the conclusion sets the experiment results realistic with the theory. (6)
The sources included in the analysis don’t present all the key components in the lab report where acknowledgement and methodology can be greatly mentioned. The images of the figures and the positions of the figures might have a distant relationship with writing. Methodology was not present at the report as their contents are basically divided into two parts with theory and calculation. The goal is to represent the coupled system and how they oscillate. During the calculation, the values taken from the experiment were directly matched with the theoretical point. So, it was one kind of what to come and what has come comparison experiment or the experiment of the behavior which has already given a result of how the system works. The discussion and conclusion part were together as they were not so large to discuss the whole result. The report was basically depending on theory more than the experiment analysis. Here the experiment values were just proof of the theory from the law.
Bibliography
[1], [2], [3], [4], [5], [6] Hyder, S. B. (2021, August 25). Example experiment report for Phys
342L – Purdue Physics. SCRIBD.
Full annotated Lab report :
https://drive.google.com/file/d/1Yiq6LntfareX4C1cpnuDXTigvzoO0ld5/view?usp=drivesdk
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