Simple Harmonic Motion Research Articles

How to enhance the resilience of domestic tourism?

Enhancing domestic tourism resilience (DTR) is crucial to achieving high-quality development of the tourism industry. However, owing to the vulnerability of the tourism industry during the COVID-19 pandemic, the enhancement pathways and associated mechanisms of DTR need to be further investigated. Therefore, this study measures the DTR of China's 31 provinces by creatively combining the simple harmonic motion and regime-switching vector autoregressive models and explores its characteristics to lay the foundation for an empirical analysis. Furthermore, the study empirically analyzes the enhancement pathways and associated mechanisms of DTR using a spatial econometric model. First, this study found that tourism agglomeration, specialization, and diversification determine the characteristics of dynamic response and spatial distributions of DTR. Second, from the perspective of spatial effects, DTR in one region positively impacts that in adjacent regions, and tourism agglomeration in a specific region positively impacts DTR in adjacent regions. Third, in terms of mechanisms, tourism agglomeration enhances DTR by optimizing industrial structure and improving production efficiency, whereas tourism specialization and diversification enhance DTR by improving production efficiency and optimizing industrial structure, respectively. These findings provide information for the enhancement of DTR and achievement of high-quality development of the tourism industry.

Role of Cosmological Models in Organic Evolution in Space

Using the dynamic Friedman-Robertson-Walker Cosmological Model of the universe, the possibility of organic evolution in Space in the early universe is explored. According to this model, the universe is expected to perform simple harmonic motion between expansion and contraction. At the end of contraction, the universe assumes the smallest possible finite size with no boundary, while the entire mass of the universe gathers together as gravity particles, or gravity waves, at the center of gravity of universe. As soon as the density of the gravity particles is extremely high and the temperature reaches the flame temperature, a sudden violent explosion hurls the entire material into space uniformly in all directions when the expansion starts. It is in this period of expansion where the precursors of DNA/RNA, such as water, oxides of phosphorus, sugars, heterocyclic bases, compounds of nitrogen, etc. are formed.

Personalized assist-as-needed dressing assistance robot without human modeling using Rowat-Selverston CPG controller

Dressing is a critical component of Activity of Daily Living (ADLs). The development of assistive technology for dressing tasks is urgently needed from the viewpoint of privacy, for example, to prevent the wearer from being seen in the nude. Despite their importance, these technologies are underutilized in garment donning compared to other ADLs. The reasons for the lack of utilization of assistive technology are that the task is complex, as it involves handling individuals with large individual differences in height and symptoms and requires manipulation of flexible clothing. Addressing these variances presents a formidable academic challenge. Our previous study identified periodic patterns in human movements during robot-assisted dressing and noted individual variability in these patterns. Capitalizing on this finding, we propose a novel control strategy for a robot that adapts to individual needs during dressing, employing the ‘Assist-As-Needed’ (AAN) principle from physical therapy. The proposed control method uses Central Pattern Generators (CPG) that can be synchronously controlled in response to external forces, enabling model-free control without human modeling. We utilize the Rowat-Selverston CPG model, which is recognized for its adaptive response to human motions in human-robot interactions such as with handshaking robots. A simulator of the Rowat-Selverston CPG was created. The output of the CPG was confirmed by inputting the data set obtained in previous studies, and the parameters were adjusted. The CPG output was then applied to the recorded target joint trajectory for the dressing assistance. We prepared a replay of the default trajectory, a trajectory with simple harmonic motion applied, and a trajectory with CPG output applied, and confirmed whether individual adaptation according to the AAN was possible through subject experiments. The experimental results showed that the Rowat-Selverston CPG control method enables individual adaptive dressing assistance according to the AAN principle. This study summarizes these methods and results and contributes to the realization of an individually adaptive system that follows the AAN principle, especially in developing assistive technology.

Squeeze force of a Maxwell fluid between circular smooth surfaces with simple harmonic motion

The force and mechanical power required to maintain the simple harmonic motion (SHM) of the upper circular surface squeezing a viscoelastic fluid film is analyzed. The amplitude of the displacement of the upper surface is very small compared to the gap width as a function of time. The smoothness of the upper and lower surfaces is characterized by the slip model with two constant parameters, a slip length and a critical surface shear stress. The nonlinear convection terms in the momentum equation are neglected since the viscous forces dominate the inertial forces. The acceleration and deceleration terms are retained since the upper plate oscillates harmonically and the velocity in the fluid is strictly periodic. An exact solution of the governing equations is found as a function of the Deborah number, the Womersley number, the slip length, and the critical surface shear stress. A circular region without slip condition, bounded by a time-dependent radius, appears when the shear stress of the fluid does not exceed a critical surface shear stress. In addition, an annular region with slip up to the radius of the disk appears when the critical surface shear stress is exceeded. Our results show that viscoelastic and hydrophobic effects together with the Womersley number and a critical surface stress cause changes in the amplitude and phase lag of the waveform of the time-dependent radius and the force acting on the wall surface to maintain the SHM of the upper disk.

How does the period of a pendulum vary with the number of strings?

This article serves as an extension of analysis of a simple pendulum, a typical example of simple harmonic motion and a common topic in high school physics syllabus. Since the analysis of a simple pendulum ignores the mass of the string in order to model the system as a point mass, a more complex pendulum system consisting of heavy strings and a pendulum bob is explored in this article. Based on theoretical analysis of the model, a relationship between the number of strings and the period of the pendulum is investigated. An experiment was also conducted on a pendulum system using copper wire, a glass bob, a stand, clamps, a clip and a stopwatch. To obtain more accurate results, time taken for five periods was measured three times for each number of strings. A graph is drawn based on data acquired from the experiment and the theoretically deduced relationship is therefore verified. Further study of the general expression for the period of an object that cannot be modelled as a point mass oscillating about a fixed axis is involved. Application of the principle that a change in the position of the center of mass of a pendulum causes a change in its period in Big Ben is also discussed along with a brief introduction of its pendulum structure.

Periodic Solutions of Strongly Nonlinear Oscillators Using He’s Frequency Formulation

In this paper, we address several scientific and technological challenges with a novel non-perturbative approach (NPA), simplifying processing time compared to traditional methods. The proposed approach transforms nonlinear ordinary differential equations into linear ones, akin to simple harmonic motion, producing a new frequency. This method yields highly accurate outcomes, surpassing well-known approximate methodologies, as validated through numerical comparisons in mathematical software. The congruence between numerical solution tests and theoretical predictions further supports our findings. While classical perturbation methods rely on Taylor expansions to simplify restoring forces, NPA also enables stability analysis. Thus, for analyzing approximations of highly nonlinear oscillators in mathematical software, NPA serves as a more reliable tool.

Exploring the Beauty of Mathematics: the Application of Rolle's Theorem in Simple Harmonic Motion and Its Value in Civic Education

Exploring the Beauty of Mathematics: the Application of Rolle's Theorem in Simple Harmonic Motion and Its Value in Civic Education

Demonstrating beat phenomenon and Lissajous figures with hard disk drive voice-coil motors

Voice coil motors (VCMs) in mechanical hard disk drives can be used as the adjustable-electric tuning fork driven by alternating signals due to their unique structure and movement. The VCM component is modified to pull the laser or mirror for phase-adjustable simple harmonic motion (SHM). Lissajous experiments using the traditional tuning fork for active vibration can be achieved by VCMs with the help of a laser and a scrollable phosphorescent screen. The demonstrations of beat and Lissajous figures with the double oscillating mirrors method are analysed. The VCM can not only drive the mirror but also drive the laser or another VCM component. Based on this carrying capacity, the demonstration method of a single oscillating mirror has been proposed. Furthermore, one VCM can support another with a laser, which will exhibit the composition of two rotary SHMs more intuitively. The new method is beneficial for students to understand and practice the composition of SHMs from a new perspective.

Pengaruh Minat Belajar Terhadap Hasil Belajar Peserta Didik Melalui Penerapan Model Inkuiri Terbimbing Berbantuan Simulasi PhET Pada Materi Gerak Harmonik Sederhana

The problem that is often faced is that many students are less interested and less motivated in learning physics, especially on the concept of simple harmonic motion. This has a negative impact on their learning outcomes, as indicated by low test scores and overall academic achievement. Therefore, an intervention is needed that can improve students' interest in learning and learning outcomes. This study aims to determine the interest and learning outcomes of physics students in class X IPA 6 SMA Negeri 2 Kupang in the guided inquiry learning model assisted by PhET simulation on simple harmonic motion material. This research is a descriptive quantitative study with a simple regression approach that aims to determine the effect between the variable of interest in learning on the variable of learning outcomes. The results of descriptive test analysis for interest variables and learning outcomes showed that the average percentage of interest in learning on pretest was 61% (high category) and on posttest was 72% (very high category); the average percentage of learning outcomes on pretest was 22 (low category) and on posttest was 86 (very high category). The regression test results show a significant effect of learning interest on student learning outcomes on simple harmonic motion material in guided inquiry learning assisted by PhET simulation. The application of guided inquiry learning model assisted by PhET simulation can increase students' learning interest, which in turn significantly improves their learning outcomes on simple harmonic motion material.

A Complete Arduino-Based Mathematical Pendulum Experiment Tool with Real-Time Data Acquisition Using an Excel Spreadsheet

It is very important for students to understand the concept of simple harmonic motion, such as a mathematical pendulum. Students need an experiment tool on mathematical pendulums that is capable of providing measurement results of various physical quantities of mathematical pendulums accurately and precisely. This research aims to (1) describe the specifications of an Arduino-based mathematical pendulum experiment tool, (2) describe the results of measurements of acceleration due to gravity, and (3) describe the effect of changes in deviation on the period at small angles. This research used the experiment method. The research results showed that (1) the Arduino-based mathematical pendulum experiment device is equipped with an HC-SR04 ultrasonic sensor to measure the length of the string and an FC-51 infrared sensor to measure the period with a precision of 94.9% and accuracy of 99%, (2) the average result of acceleration due to gravity measurements at various string length was (9.72 ± 0.19) m/s<sup>2</sup>,and (3) the mathematical pendulum period between angles of 1-13 degrees did not show a significant difference, showing that at small angles, the oscillation period is not affected by deviation.

Development of Dispersion Calculator SAFEDC of Guided Wave with Complex Material and Waveguide

The propagation characteristics of guided waves (GW) are related to both the material, loading and geometry parameters. Correct understanding of GW is the key step towards further GW-based structural health monitoring. A dispersion calculator of GW propagating in the complex geometry with viscoelastic and anisotropic material parameter in the open waveguide is developed based on the semi-analytical finite element (SAFE) method and perfectly matched layer (PML). By assuming the simple harmonic motion along the propagation direction and adopting the mesh discretization in the cross section, SAFE features the capability of GW calculation in the complex waveguide at only a cost of limited calculation resources. Hence, besides the capabilities of the most off-the-shelf tools focusing on the analytical solution of GW in simple plate or pipeline, the developed algorithm further offers the solution of GW in open waveguide with laminates of arbitrary ply stacking sequences and in arbitrarily complex cross section. Quadratic one-dimensional and triangular elements are adopted to automatically discretize the plate structure and complex cross section, respectively. The obtained results of GW in plates are in a good agreement with the results obtained with the off-the shelf-tools that adopt analytical derivations, and show stronger robustness of mode searching and sorting by avoiding the complex root-finding procedure required in the analytical derivation. The most GW features, including phase velocity, group velocity, attenuation, wave structure in terms of displacement, stress, and strain, and animation of wave propagation are directly calculated. All these functions are integrated and updated in the previously developed freeware SAFEDC, whose 1st version SAFEDC v1.0 was published in September 2023.

General characterisation of Hamiltonians generating velocity-independent forces

Dynamics generated from Hamiltonians enjoy potential pathways to quantisation, but standard Hamiltonians are only capable of generating conservative forces. Classes of Hamiltonians have been proposed in Berry and Shukla (2015 Proc. R. Soc. A 471 20150002) capable of generating non-conservative velocity-independent forces. Such Hamiltonians have been classified in the past, under the strict assumption that they are polynomial in momentum. This assumption is relaxed here to analyticity. In doing so, broader classes of Hamiltonians are discovered. By considering the Hamiltonian as a function of state space without introducing the Lagrangian and constructing a metric-like tensor, we develop strong general constraints on Hamiltonians generating velocity-independent forces and exhibit a surprising dichotomy between classes of such Hamiltonians. These results are applicable to any spatial domain of any dimension admitting well-defined Hamiltonian dynamics. As an example application, we apply these constraints to classify all Hamiltonian velocity-independent forces in two spatial dimensions, as well as all such Hamiltonians which do not generate an isotropic simple harmonic motion. The case of one spatial dimension is also discussed for the sake of completeness.

The game with a "life-line" for simple harmonic motions of objects

The game with a "life-line" for simple harmonic motions of objects

Two-Method Indoor Laboratory Instruction: How Effective Is It on Secondary School Students’ Performance in Physics?

This study probed the effectiveness of two-method indoor laboratory instruction on secondary school students’ performance in physics in Jos Metropolis, Nigeria. The quasi-experimental research design of the non-equivalent control group pre-test, post-test type was employed. The population for the study comprised 1,112 senior secondary two students offering physics in 18 schools in Jos metropolis, with the schools purposively obtained. The study sample consisted of 80 SSS II students obtained from two intact classes, one class each from two schools selected using simple random sampling technique. Two research questions were raised and two hypotheses were formulated. Physics Performance Test (PPT) was the instrument validated and used to gather data. The test-retest method was used to obtain the reliability of PPT and its coefficient was computed as 0.73 using Kuder-Richardson formula 21 (K-R 21). Mean and standard deviation were used to answer the research questions while independent t-test of difference and Analysis of Covariance (ANCOVA) were the statistical tools used to test the hypotheses at 0.05 levels of significance. The results revealed that students taught concepts of simple harmonic motion and elasticity using group indoor laboratory method performed better than their counterparts taught using individual indoor laboratory method; although male students performed slightly higher than their female counterparts after exposure to the two methods, gender was found to have no interaction effect on their performance; there was a significant interaction effect of treatments and gender on students’ performance in the study area, with the methods as source of interaction effect. Based on the findings, recommendations were made, which include that curriculum developers should ensure that laboratory teaching methods are included in physics curriculum in order to enhance students’ performance in the subject.

Simple harmonic motion studied on spring-mass system using Phyphox application

Simple harmonic motion experiments have been conducted using a smartphone-based spring-mass system with the Phyphox application. This research aims to investigate the relationship between the mass of an object and the period and frequency of oscillations and determine the spring constant using smartphone-based experimental equipment. The method uses the "spring" feature in the Phyphox application to visualize oscillatory movements in real-time and measure the period and frequency of oscillations. The experimental results show that the spring constant obtained from the smartphone-based experiment is 9.51 N/m, with a difference of 1.25% compared to the Hooke's Law experimental setup with the conventional method. This shows that using a smartphone-based experimental setup can be a better alternative for conducting physics experiments requiring high accuracy.

The Effect of Flipped Classroom Learning Assisted by Computer Simulation on Students' Comprehension of Simple Harmonic Motion

Innovation in science learning is highly recommended by various studies and education experts. Through this learning innovation, teachers create learning that facilitates students' curiosity by getting them involved in learning, which ultimately helps them understand science in depth. However, the current trend is that science classes "fail" to create innovative learning that can foster students' interest in science, so that many students do not understand science well. This research aims to determine the impact of flipped classroom learning on simple harmonic motion material assisted by computer simulations on students' conceptual understanding. A pre-experiment with a one-group pretest-posttest design was used in this research. Class X of the MIPA program was chosen as the experimental object in this research, and 30 students were used as samples. The test given is a multiple-choice test with explanations. The results showed that the average post-test score was better than the pre-test. The N-gain score is 0.79, which indicates that there is an increase in students' understanding in the high category. This shows that flipped classroom learning assisted by computer simulations can increase students' understanding of the concept of simple harmonic motion. By implementing computer simulation activities that are integrated into flipped classroom learning, learning alternatives can be enriched to help students understand science.

Fractal Schrödinger equation: implications for fractal sets

This paper delves into the world of fractal calculus, investigating its implications for fractal sets. It introduces the Fractal Schrödinger equation and provides insights into its consequences. The study presents a general solution for the time-dependent Schrödinger equation, unveiling its core aspects. Exploring quantum mechanics in the context of fractals, the paper analyzes the probability density of the radial hydrogen atom, unveiling its behavior within fractal dimensions. The investigation extends to deciphering the intricate energy levels of the hydrogen atom, uncovering the interplay of quantum mechanics and fractal geometry. Innovatively, the research applies the Fractal Schrödinger equation to simple harmonic motion, leading to the introduction of the fractal probability density function for the harmonic oscillator. The paper employs a series of illustrative figures that enhance the comprehension of the findings. By intertwining quantum mechanics and fractal mathematics, this research paves the way for deeper insights into their relationship.

Analyzing Physics Experiment using Sensor Smartphone in Traveling Carnival

Smartphone integration for high school students has significant potential in physics learning. This research aims to analyze smartphone sensor data in the context of physics experiments carried out at traveling carnivals. This research uses experimental methods to compare smartphone sensor data collected via the Phyphox application with video analysis data obtained using Tracker software. The research results show the effectiveness of smartphone sensors in several carnival games, including simple leg swings, bicycle spins, kora-kora vehicles, and merry-go-rounds. Smartphone sensors can show graphs of simple harmonic motion, angular velocity, and centripetal acceleration on the game vehicle. However, limitations arise in the case of Ferris wheels and mini Ferris wheels, where smartphone sensors show reduced effectiveness caused by the instability of passenger seats during the ride. This research suggests avenues for further exploration by computing physical quantity values derived from smartphone sensor data, offering insights into potential improvements and applications in dynamic environments such as theme parks.

A mechanical device to demonstrate the composition of two simple harmonic motions

The slot link mechanism can project uniform rotation to a simple harmonic motion (SHM), based on which, the device including two sliding table systems has been prepared. These two sliding table systems can be stacked up and down, and each of them can produce a tunable mechanical SHM using a stepper motor. When the upper sliding table system is attached to the lower one and both are turned on, the motion of the sliding table of the upper component is the composition of the two SHMs. With the help of a self-powered LED, a violet laser, and a movable phosphorescent foil, this mechanical device can visualize the composition of the SHMs in the same and mutual perpendicular directions including the beat phenomenon and Lissajous figures. In addition to demonstrating several typical compositions of two SHMs, this device can also highlight the vector characteristics of mechanical vibration and demonstrate the tilted Lissajous figures.

The Effectiveness of the POGIL Learning Model on Simple Harmonic Motion Topic to Enhance Students' Science Process Skills

The lack of training in students' science process skills indicators in physics subjects has resulted in a majority of students in one of the high schools in Banjarmasin, grade X MIPA, having relatively low science process skills. This study aims to describe the effectiveness of the POGIL learning model and assess the achievement of students' science process skills. This study used a one-group pretest-posttest design. The results showed that using the POGIL model based on the n-gain calculation had a high effectiveness category with a value of 0.73 and trained students' science process skills, as indicated by an increase in the achievement of science process skills, which had a very good category. Based on these results, using the POGIL model can provide benefits in practicing students' science process skills.