Application of Image Analysis Methods

Study Case Application of Image Analysis Methods to Analyze Simple Harmonic Motion in Springs and Pendulums Michael Kurniawan (2018123456) University of Cincinnati, 2600 Clifton Ave, Cincinnati, OH 45221, United States kurniaml@mail.uc.edu Abstract Simple harmonic motion is one of the fundamental concepts in physics, which forms the basis for understanding more complex phenomena such as oscillation and damping. This study aims to examine the effect of mass on the dynamics of springs and simple pendulum motion by utilizing digital image analysis methods. In this study, a cell phone camera was used to record the motion, and ImageJ software was used as the main analysis tool. This research produced an alternative approach to analyzing the results of simple harmonic motion experiments, which can be used as a substitute for conventional methods based on manual measurements using a ruler and stopwatch. The results of the study show that the image analysis method provides better accuracy in studying the characteristics of simple harmonic motion. Keywords: simple harmonic motion, spring, pendulum, image analysis, ImageJ software INTRODUCTION Education has always been an important topic for research and development. Although the education system continues to evolve in line with technological advances and societal developments, there are still various challenges that need to be overcome, such as disparities in the quality and access to education between regions, uneven curricula, and limited learning support facilities . As stated by Vito et al. (2015), the educational gap between urban and rural areas is not only related to access to schools but also includes facilities, teaching staff, and laboratory infrastructure. MICHAEL KURNIAWAN 1 Study Case Limited laboratory facilities often become an obstacle in conducting experiments, especially in the field of physics. Therefore, teachers are expected to be able to innovate by utilizing technology and resources that are easily accessible around them. One innovative approach that can be applied in dynamics experiments is the use of digital image analysis methods, which only require a smartphone and computer software. Image analysis is the process of extracting information from digital images to produce quantitative data that can be used in decision making. According to Ahmad and Firdaus (2005), an image is a visual representation or imitation of an object. This method has been widely used in various disciplines such as astronomy, biology, and physics. In physics, especially in the study of motion, manual measurements are often difficult to perform with high precision, especially if the motion occurs in a very short time. Therefore, digital image-based methods can be a more effective solution than the use of conventional tools such as rulers and stopwatches. In addition to improving accuracy, this method also enables observation of objects that are difficult or dangerous to measure directly. For example, in wildlife biology research (Putra et al., 2016), image analysis can be used to obtain motion data without direct contact with the object. In this study, we applied image analysis methods to study simple harmonic motion (SHM) in spring and pendulum systems. Several software programs that can be used for image analysis include Free Video to JPG, ImageJ, and MATLAB. In this study, Free Video to JPG was used to extract frames from the video, and ImageJ was used to analyze the position and displacement of the object digitally. The combination of these two applications provided detailed and accurate results for the study of simple harmonic motion. Simple harmonic motion is a regular back-and-forth motion through an equilibrium point, where the period of oscillation is constant. If a motion repeats periodically in the same time interval, the motion is categorized as periodic motion, and if it occurs regularly, it is called harmonic motion. In the context of secondary education, this topic is an important part of the physics curriculum and is usually observed through experiments with springs and simple pendulums. However, conventional measurements with a stopwatch are often prone to human error. Therefore, image analysis methods offer a more accurate and efficient alternative for studying this phenomenon. MICHAEL KURNIAWAN 2 Study Case RESEARCH METHODS The stages of this research include: 1. Preparation of tools and materials. 2. Preparation of experimental instruments. 3. Conducting experiments. 4. Image processing using ImageJ software. 5. Data analysis. 6. Drawing conclusions. The research equipment setup is shown in Figure 1. The circuit consists of: 1. a pendulum with a load ready to be displaced, 2. a static stand to support the pendulum, and 3. a cell phone camera used to record the pendulum's movement within a certain time interval. The camera used has a resolution of 13 megapixels with image dimensions of 4224 × 3136 pixels. The experimental design for the spring system was made using a similar principle. For pendulum measurements, variations in rope length of 36 cm, 40 cm, and 48 cm were used, with an initial angle of deflection of 10°. Meanwhile, for the spring system, load mass variations of 70 g, 100 g, and 250 g were used, with an initial displacement of 3 cm. Each experiment was recorded using a cell phone camera, then the video was transferred to a computer for processing. The video was converted into a series of images using Free Video to JPG, and position analysis against time was performed with ImageJ to obtain a displacement graph as a function of time. Figure 1. Simple pendulum motion recording apparatus: 1 pendulum with load ready to be displaced, 2. static stand, 3. cell phone camera as recording device. MICHAEL KURNIAWAN 3 Study Case RESULTS AND DISCUSSION 3.1 Spring Based on the experimental results, the load mass was found to have a significant effect on the oscillation characteristics of the spring system. Figure 2 shows the change in load position over time during simple harmonic motion. From the graph, it can be observed that the mass of the load directly affects the dynamics of spring motion. The greater the mass of the load suspended, the smaller the frequency of oscillation produced, so that the vibration period becomes longer. In other words, the spring oscillates more slowly as the mass of the load increases. In the experiment with a mass of 70 g, the spring showed relatively fast acceleration, while with a mass of 250 g, the oscillation became slower with a larger range of displacement on the graph. These results are consistent with the theory of simple harmonic motion, where the frequency f is related to the spring constant k and mass m through the equation: 𝑓= 1 𝑘 √ 2𝜋 𝑚 This equation shows that an increase in mass (m) will decrease the frequency of oscillation, consistent with the experimental observations. Figure 2. Change in spring length over time for (a) m = 70 g, (b) m = 100 g, and (c) m = 250 g. MICHAEL KURNIAWAN 4 Study Case 3.2 Simple Pendulum The experimental results for a simple pendulum show the relationship between the angle of deflection and time for various string lengths. In Figure 3, for a string length L = 36 cm, the maximum angle of deflection on the positive side occurs at 0.24 s with a deflection of 8.13°, while the smallest deflection occurs at 3.04 s with a deflection of 0.45°. On the negative side, the maximum deflection is reached at a time of 0.56 s with a value of –4.33°, and the minimum deflection at a time of 0.84 s is –0.76°. Figure 3. Relationship between the angle of deviation and time for L=36“ cm”. In Figure 4, for a string length of L=40“ cm”, the maximum deviation on the positive side occurs at 0.08 s with a value of 11°, and the smallest deviation occurs at 3.76 s and 3.85 s with a value of 0.28°. On the negative side, the largest deviation occurs at 0.32 s with a value of –7.55°, and the smallest deviation occurs at 1.84 s and 2.32 s with a value of –0.14°. Figure 4. Relationship between the angle of deviation and time for L=40 cm. In Figure 5, for a string length of L=48 cm, the maximum deviation on the positive side occurs at 0.6 s with a value of 8.42°, while the smallest deviation occurs at 3.84 s with a value of 0.23°. On the negative side, the largest deviation occurs at a time of 0.84 s with a value of –3.78°, and the smallest deviation occurs at a time of 6.0 s with a value of –0.8°. MICHAEL KURNIAWAN 5 Study Case Figure 5. Relationship between the angle of deflection and time for L=48“ cm”. Finally, Figure 6 shows the results for a string length of L=50“ cm”. The maximum deflection on the positive side occurs at 1.25 s and 1.46 s with a value of 11.6°, while the minimum deflection is recorded at 8.77 s with a value of 0.45°. For the negative side, the maximum deviation occurs at 0.62 s at –10.1°, and the smallest deviation at 2.29 s at –0.22°. Figure 6. Relationship between the angle of deviation and time for L=50“ cm”. In general, the longer the pendulum string, the greater the period of oscillation. This result is in line with the theory that the period of a simple pendulum (T) depends on the length of the string (L) and the acceleration due to gravity (g) according to the equation: 𝐿 𝑇 = 2𝜋√ 𝑔 Thus, the experimental results successfully show that the variation in string length is directly proportional to the period of oscillation, as predicted by theory. MICHAEL KURNIAWAN 6 Study Case CONCLUSION The application of image analysis methods using ImageJ software has been proven to provide more comprehensive and accurate results compared to conventional methods. With a single experiment, a large amount of data can be obtained, enabling more indepth analysis of the characteristics of simple harmonic motion. From the observation results: • Oscillation in a spring system depends on the mass of the load used. The greater the mass, the slower the frequency of oscillation and the greater the period of motion. • Image-based analysis is able to reveal phenomena such as damped oscillations and external disturbances that are not easily observed with a stopwatch and ruler. • The results for the pendulum system show a consistent relationship between the length of the string and the period of oscillation, in accordance with the theory of simple harmonic motion. Thus, the ImageJ-based image analysis method can be used as an effective alternative in physics experiments, especially for the study of simple harmonic motion in spring and pendulum systems. REFERENCE MICHAEL KURNIAWAN 7 Study Case MICHAEL KURNIAWAN 8