Simple Harmonic Motion Research Articles

Is the Combination of Linearized Theoretical Analysis and Sand Column Experiment Always Suitable for Estimating the Complex Effective Porosity?

AbstractGroundwater hydrodynamics are significantly affected by the capillary effect when groundwater table approaches sand surface. A complex effective porosity was suggested to replace the specific yield to represent the capillary effect based on varieties of sand column experiments, and its estimation is based on the assumption that the response of time‐varying groundwater table is a simple harmonic motion. Nevertheless, groundwater hydrodynamics always consist of multiple harmonic components, which should be further examined. In this study, we first conducted laboratory sand column experiments with respect to different periodic oscillation conditions. Then, a fast Fourier transformation algorithm was applied to analyze the measured groundwater table, upon which the high order harmonic components under high frequency wave conditions was demonstrated. Subsequently, based on a perturbation approach, we presented a third order analytical solution of time‐varying groundwater table under a simple harmonic oscillation. The gradient descent method was applied to estimate the complex effective porosity by fitting the high order analytical solution to the experimental data. In addition, effects of various parameters, representing different driving head conditions and sediment properties, were testified through parametric studies, which demonstrates high order harmonic components should not be neglected under the conditions of large relative amplitude of driving head, short period oscillation, and the ratio of hydraulic conductivity to dynamic effective porosity being around 1 m/s, for example, in the scenarios of wave‐dominant swash zone. These new findings are of great importance to extend our understandings of the capillary effect on groundwater hydrodynamics.

Differential equations: Solving the oscillation system

The purpose of this research is to perform modeling and simulation to solve differential equations in cases of physical phenomena. The physical system studied is simple harmonic motion. The method used is the method of problem solving using computer software. The simulation uses the Matlab program by applying the Euler method. The result obtained is to distinguish the oscillator graph without any external forces with any forces. This solution helps students solve problems using computer software in giving physical meaning. Therefore, students must be trained and guided to have the ability to think to make it easier to solve problems with the help of computers.

Classical Doppler Effect in Some Accelerated Systems

In this note, the classical Doppler shift for some accelerated mechanical systems is considered under a common graphical approach. In one dimension, we study uniform accelerated motion and simple harmonic motion. In two dimensions, uniform circular motion and pendular motion are considered. In each case, an elementary treatment shows that the period (and frequency) measured by an observer at rest depends on the straight paths of two consecutive signals between source and observer, with due consideration of the acceleration.

Discussion on Spontaneous Parametric Down-conversion (SPDC) Based on Parametric Oscillator Model

In this article, we use the theory of simple harmonic motion to estimate the vibration energy of Boron atom. Subsequently we employ the parametric oscillator model to discuss photon pairs with wavelength of 710 nm. When a laser with wavelength of 355nm illuminates the barium meta-borate crystal, parametric resonance could lead to the effect of spontaneous parametric down-conversion.

Dynamic tree branch tracking for aerial canopy sampling using stereo vision

Maintaining the massive forests of the forestry industry requires physical samples from the tree canopy to enable breeding, genetics research and monitoring of diseases. An autonomous Unmanned Aerial Vehicle (UAV) canopy sampling solution requires locating and tracking a highly unstructured, moving object against a dynamic, cluttered background. The developed algorithm utilises stereo vision techniques to reconstruct a 3D point cloud of the target branch and subsequently estimate the intercept point location. The optimal parameters are selected by quantifying the accuracy against ground truth obtained from motion capture. Since wind will likely affect the tree canopy during sampling, the branch will exhibit some sway motion which can be modelled as simple harmonic motion. Hence, a linear Kalman filter is formulated to estimate the sway parameters. With the branch 1m from the camera, the average error is 41mm for sway amplitudes between 50mm and 250mm with a plain background. When tested with a cluttered background, the reduced contrast results in higher standard deviations. Overall, the developed Kalman filter significantly reduces the intercept point error standard deviation, averaging 17% and 33% reductions for plain and cluttered backgrounds respectively. Subsequent outdoor testing verified the capability of the developed algorithm to estimate the branch trajectory to well within the maximum gripper opening of 115mm.

Regional economic resilience in China: measurement and determinants

ABSTRACT Resilience is system specific rather than shock specific. This study proposes a new measure of engineering resilience based on the theories of simple harmonic motion and regime switching, and it examines the determinants of resilience among China’s regional economies to the 2008 subprime crisis. Enhancing industrial diversity, human capital stock, trade openness and financial liberalization can improve economic resilience. Pre-crisis economic performance had a negative effect on regional economic resilience in China. More efforts are needed to enhance regional economic resilience in China by fostering entrepreneurship. The results provide information for policies to address external shocks and promote sustainable regional economic development.

Liquid oscillating in a U-tube of variable cross section

A liquid is set into oscillations in a vertical manometer of smoothly varying cross-sectional area open at both ends to the atmosphere. Ignoring viscous damping, the displacement of either free surface and the pressure at any point in the liquid can be calculated using the unsteady Bernoulli equation which is shown to be consistent with conservation of mechanical energy. If the cross section is constant, the equations are analytically solvable; simple harmonic motion is found for the surface displacement as a function of time, and the pressure variation as a function of depth is in accordance with Newton’s second law. More generally, however, numerical solution of the equations is necessary, as illustrated for the example of a U-tube whose radius is linearly tapered from one end to the other. The level of presentation is appropriate for an upper level undergraduate course in fluid mechanics.

The impact of learning management system implementation on students’ understanding of mechanics concepts

The Learning management system (LMS) is an effective model of learning for solving the teaching problems. Effective learning will help students achieve better understanding of the concept. This article discusses the use of LMS in teaching mechanics and its effect on student understanding. This quasi-experiment research used one group post-test design. The sample used was 21 students from one of the higher educations in Mataram, Indonesia. The instrument used was the conceptual understanding test in multiple choices. The test consists of 30 questions which are divided into three mechanics concepts, namely Newton’s Laws of Motion, Work and Energy, and Simple Harmonic Motion. Each data was analyzed using simple statistics. The findings showed that the use of LMS had a positive impact on students’ understanding of each topic of mechanics concepts. The highest average score on the topic of Work and Energy. The lowest average score is on Newton’s Laws of Motion. LMS is an alternative platform for developing students’ understanding of concepts in each cognitive aspect.

Increasing HOTS of High School Students Using Mobile Technology and Scaffolding Approach: Study on Physics Learning

Improvement, development, and growth of a country cannot be separated from the quality of its human resources. This is even more so for a country that will face a population demographic bonus like Indonesia, which requires excellent and increasing quality of human resources so that they are always able to compete. Education is one of the factors that plays an important role in advancing the quality of human resources. This study aims to develop an Android-based learning media application on simple harmonic motion physics material and is used to improve the HOTS ability of students by learning using the scaffolding approach. This study is an R&D with a 4D model consisting of the Defining, Designing, Developing, and Disseminating stages. The operational test at the Developing stage was carried out using an experiment with the Pretest-Posttest Control Group design. The product in this study is an Android-based physics learning media application on simple harmonic motion material that has been tested for its feasibility for use in physics learning. Then, the product was tested in the field by being implemented in learning. The experimental results in the experimental class using android media and the scaffolding approach and the control class using conventional learning showed a significant difference in HOTS abilities. The implementation of Android-based physics mobile learning media and the scaffolding learning approach has a positive effect on the HOTS ability of students.

PENERAPAN PENDEKATAN SOMATIC, AUDITORY, VISUAL, INTELLECTUAL (SAVI) UNTUK MENINGKATKAN HASIL BELAJAR PESERTA DIDIK TENTANG GERAK HARMONIK SEDERHANA KELAS X SMA NEGERI 1 MENTEBAH

AbstractThis study aimed to improve the learning outcomes of class X students of SMA Negeri 1 Mentebah on simple harmonic motion material by applying the Somatic, Auditory, Visual, Intellectual (SAVI) approach. This study used a pre-experimental design with a one-group pretest-posttest design. Determination of the sample of this study using purposive intact group sampling with a total of 30 students. The measurement technique using a measuring instrument in the form of a bentul written test, a description of the data collection technique used in this study. The Wilcoxon test results obtained the asymp value. Sig. (2-tailed) of 0.000 with α = 0.005. This shows that there is an increase in student learning outcomes after applying the Somatic, Auditory, Visual, Intellectual (SAVI) approach to learning. The level of effectiveness obtained is included in the high category, namely 5.69.Keywords: Somatic Auditory Visual Intellectual (SAVI), Learning Outcomes, Simple Harmonic Motion

Real Time Measurement for Spring-Mass System: The Graphical and Mathematical Representations

Mathematics is the language of physics. The best way to describe a physical phenomenon is by describing its mathematical representations. In addition, viewing the graphical diagram of the corresponding mathematical expression is crucial to deeply understand the physical events. Therefore, setting simple experiments in real time to (1) observe the phenomena, (2) view the related diagrams, and (3) extract the mathematical representations is required. In this study, the real time and simple experimental set-up (consisting of ultrasonic sensor HC-SR04 connected to an Arduino Uno board) was designed to perceive the motion of a spring-mass system. The spring force, which is equal to the object’s weight, and displacement or spring elongation data were recorded for the object (with varying mass) attached to the spring. A small external downward force was given to stimulate the simple harmonic motion of the vertical spring-mass system. The displacement as the function of time of the spring-mass motion was recorded. With those measurements, the sinusoidal patterns, representing the simple harmonic motion characteristics, were also observed. The spring constants were 6.35(2) N/m and 6.26(1) N/m for the displacements measured by sensor and ruler, respectively. The periods form the angular frequency of the displacement function and from the spring constant (acquired from sensor data fitting) showed consistent results with very high accuracy. This simple experimental set-up is believed to fulfill the technological-based learning demand.

Development of Test Instruments to Analyze Higher-Order Thinking Skills Through Science-Based Literacy Learning

Higher-order thinking skills are essential skills for a pre-service teacher to have. This study aims to develop the instrument and measure the higher-order thinking skills pre-service physics teacher UIN Walisongo Semarang with science literacy-based learning using the High Order Thinking Skills instrument. The data collection method used was a test, consisting of 20 selected questions with open reasons; structured interviews with lecturers and pre-service physics teachers; and documentation to collect pre-service physics teachers’ data required for research. The test instrument developed by reacherchers and validated by expert in the field of evaluation and physics. The instrument developed was in the form of questions grids, test questions, answer keys, scoring and assessment guidelines, and guidelines for the interpretation of high order thinking skills. The results of product development obtained 14 test items representing four indicators on Simple Harmonic Motion material. The results showed that the higher-order thinking skills of pre-service physics teachers were in the poor category, with an average percentage of 39%. The highest thinking skills are in the indicators determining the period and frequency of vibrations in simple harmonic motion that is in the good category with a percentage of 60.8%. The lowest thinking skills are on the indicator of analyzing energy in simple harmonic moving objects, which are in the inferior category with a percentage of 12.8%. The results of the research show that the higher-order thinking skills of pre-service physics teachers are still low, so that lecturers need to follow up to improve higher-order thinking skills of pre-service physics teachers UIN Walisongo Semarang.

The Verification of Propotionality Between Time Period and Length of a Simple Pendulum Experiment Using Deep Neural Network

This research shows a pedagogic experimental and theoretical study of the motion of a simple pendulum, which considers the propotionality to the variables length (L) and period-time (T) of a simple harmonic motion, is presented. The study has used RELU (RECTIFIED LINEAR UNIT) activation function in deep neural network which is a branch of artificial neural network to examine the correlation between the dependent and independent variables in a simple pendulum experiment, the variables and their values was first generated from an online physics laboratory, the values and their corresponding variables were later separated into two CSV files, after which they were analyzed with the use of linear regression model in PYTHON programming language. It also applies to Physics Direct Method to represent these equations, in addition to the numerical solutions discusses. This research investigates the relationship between Length and Period using neural network models to find out a unique numerical solution by using simulation to see their behavior which shows in last part of this article. The results obtained shows that the linear approach to modeling the relationship between a scalar response and one or more variables with the RELU activation function proves their proportionality, this would be a good reference against which other results obtained from other simple harmonic motion experiments can be compared.

Slow-dissipation limit of the harmonic oscillator with general power-law damping

An approximate solution is presented for simple harmonic motion in the presence of damping by a force which is a general power-law function of the velocity. The approximation is shown to be quite robust, allowing for a simple way to investigate amplitude decay in the presence of a general type of weak, nonlinear damping.

Pendulum physics poetry: Thus, dances the horizon!

I write short stories and poems in my mother tongue Tamil and I admire the works of Carlo Rovelli and Fritjof Capra, so I decided to write a poem about physics involving the concepts of simple harmonic motion, simple pendulum forces (shown in Fig. 1) and energy.

Parametric Approach for Satellite Relative Orbit Designs and Constellations

This paper proposes a dynamics solution that creates an identical constellation pattern of multiple satellites with the parameterization of relative motion dynamics. The parameterization illustrates that the complexity of relative motion dynamics is interpreted by a Ptolemaic model of an epicycle and deferent system. All possible relative orbits can be represented by a hypo-epi curve or a deformed curve on the x-y plane and a simple z-axis harmonic oscillator motion. The designed relative orbits are used to create identical constellation patterns of multiple satellites, called parametric constellations in this study, by closed-form formulas and satellite phasing rules obtained from the geometrical relationship and periodic conditions. In conclusion, the resulting solution contributes to solving technical dynamics and tracking problems by simply designing complex relative motions in free space.

Analysis of turbulent structures around a rectangular prism building model using spectral proper orthogonal decomposition

This paper presents a study on the turbulent structure of the wind velocity field around a rectangular prism building model, calculated using large-eddy simulation. Spectral proper orthogonal decomposition (SPOD), a technique to perform proper orthogonal decomposition (POD) in the frequency domain, was applied to extract the physical phenomenon with the largest kinetic energy from the velocity field on a plane near the ground. The obtained fluctuation modes were periodic functions, sorted by frequencies, and provided an insight into the spatiotemporal structures of various physical phenomena within the turbulence field, including the Kármán-type and arch-type vortex shedding and the flow separation phenomenon. The obtained eigenvalues depicted the kinetic energy distribution for all fluctuation modes, which was considered useful for understanding pedestrian-level wind. The results were compared for two cases (with and without fluctuation at the inflow boundary), which depicted the effect of the inflow fluctuation on the turbulent structures around the building. Additionally, for each physical phenomenon, the two modes calculated by POD were found quite similar to the real and imaginary parts of the SPOD eigenfunction. This indicates that POD needed two modes to depict each of the simple harmonic motions which were successfully detected by SPOD.

New formulation of the finite depth free surface Green function

For a pulsating free surface source in a three-dimensional finite depth fluid domain, the Green function of the source presented by John [F. John, On the motion of floating bodies II. Simple harmonic motions, Communs. Pure Appl. Math. 3 (1950) 45-101] is superposed as the Rankine source potential, an image source potential and a wave integral in the infinite domain $(0, \infty)$. When the source point together with a field point is on the free surface, John's integral and its gradient are not convergent since the integration $\int^\infty_\kappa$ of the corresponding integrands does not tend to zero in a uniform manner as $\kappa$ tends to $\infty$. Thus evaluation of the Green function is not based on direct integration of the wave integral but is obtained by approximation expansions in earlier investigations. In the present study, five images of the source with respect to the free surface mirror and the water bed mirror in relation to the image method are employed to reformulate the wave integral. Therefore the free surface Green function of the source is decomposed into the Rankine potential, the five image source potentials and a new wave integral, of which the integrand is approximated by a smooth and rapidly decaying function. The gradient of the Green function is further formulated so that the same integration stability with the wave integral is demonstrated. The significance of the present research is that the improved wave integration of the Green function and its gradient becomes convergent. Therefore evaluation of the Green function is obtained through the integration of the integrand in a straightforward manner. The application of the scheme to a floating body or a submerged body motion in regular waves shows that the approximation is sufficiently accurate to compute linear wave loads in practice.

INVESTIGATION OF UNDERGRADUATE STUDENTS CONCEPTUAL UNDERSTANDING ABOUT SIMPLE HARMONIC MOTION ON MASS-SPRING SYSTEM

Simple Harmonic Motion (SHM) is one of a primary physics topic that underlies other concepts and is closely related to everyday life and technology. It is used to understand the phenomena of mechanical motion, sound, light, and quantum theory, in particular, harmonic oscillators. This study aimed at investigating students conceptual understanding of simple harmonic motion on the mass-spring system. Data collection was made using tests and interviews. The research subjects consisted of 49 students at a university in Jakarta. The instruments used were multiple-choice tasks. The results of the investigation showed that most students have not been able to name the basic concepts of simple harmonic motion, determine the magnitude of the acceleration of objects due to oscillation, and find the scope of the oscillation period. The results show that the average achievement of students is less than 50%. Lack of understanding of student conception is caused by students not being able to relate previous insights (such as Newtons law and Hookes Law) with strategies for solving problems.

Tidal Effect on Groundwater Fluctuations and Saltwater Intrusion in Coastal Heterogeneous Aquifers. (Dept. C. ( Irrigation And Hydraulics ))

Groundwater table and saltwater wedge in coastal areas are commonly affected by tidal waves fluctuations. In this research, for the first time, a two-dimensional numerical model in plan is developed for simulating both the tidal fluctuation of the beach groundwater table and movement of interface between saltwater and freshwater in both coastal confined and unconfined heterogeneous aquifers. The sharp interface philosophy is adopted to simulate dynamics of freshwater flow. Tidal waves are simulated by simple harmonic motions in time. The solution is based on an approach of separating large and small time scales motions of groundwater fluctuations. The proposed model consists of two sub-models. The first one applied Finite Element Method (FEM) to simulate the hydraulic responses of the aquifer in large time scale and it is coupled with Finite Difference Method (FDM), in the second sub-model, to simulate the corresponding ones in small time scale. The model is verified against analytical solutions presented by other previous researchers in case of homogenous aquifer. To simulate the aquifer heterogeneity, unconditional random log-hydraulic conductivity fields are generated to present different hydraulic conductivity realizations for the aquifer under consideration. The application is carried out on both the hypothetical confined aquifer and the real Quaternary unconfined aquifer in El Arish-Rafah area, Egypt. Results show that both the groundwater fluctuation and saltwater intrusion due to tidal waves are affected by the aquifers heterogeneity and the tidal waves effects in confined aquifers are more significant than in unconfined aquifers.