## The frequency of free oscillation of a damped simple pendulum with large amplitude depends on its amplitude unlike the amplitude-independent frequency of oscillation of a damped simple harmonic osc.

Free Oscillations of a Damped Simple Pendulum: An Analog Simulation Experiment

## Experiments with a damped simple pendulum were carried out and modelled for large amplitude motion with physics students in a mechanics laboratory course of the first year of the university.

Using a large amplitude pendulum in a learning cycle strategy

## This study aimed to investigate the chaos behavior resulted from damped driven nonlinear simple pendulum motion, which was simulated by using Mathematica. 本研究旨在研究由阻尼驱动的非线性单摆运动引起的混沌行为，该运动使用 Mathematica 进行模拟。

Investigation of chaos behaviour on damped and driven nonlinear simple pendulum motion simulated by mathematica

## The response of the nonlinear simple pendulum was used for benchmarking the boundary conditions for each of the four response regimes and the test criterion was demonstrated using relevant examples. 非线性单摆的响应用于对四种响应状态中的每一种的边界条件进行基准测试，并使用相关示例演示了测试标准。

Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

## We propose a simple pendulum model that accurately captures the velocity fluctuations of the particles in still fluid and find that differences in the falling style might be explained by a closer alignment between the particle's pitch angle and its velocity vector. 我们提出了一个简单的钟摆模型，可以准确地捕捉静止流体中粒子的速度波动，并发现下落方式的差异可以通过粒子的俯仰角与其速度矢量之间的更紧密对齐来解释。

Settling behaviour of thin curved particles in quiescent fluid and turbulence

## In particular, a number of classical non-linear oscillators, such as the simple pendulum model, the van der Pol circuital model and the Duffing oscillator class are recalled from the dedicated literature and are extended to evolve on manifold-type state spaces. 特别是，一些经典的非线性振荡器，如简单的钟摆模型、范德波尔电路模型和达芬振荡器类，从专门的文献中被召回，并被扩展为在流形类型的状态空间上演化。

Synthetic nonlinear second-order oscillators on Riemannian manifolds and their numerical simulation

## This study aimed to investigate the chaos behavior resulted from damped driven nonlinear simple pendulum motion, which was simulated by using Mathematica. 本研究旨在研究由阻尼驱动的非线性单摆运动引起的混沌行为，该运动使用 Mathematica 进行模拟。

Investigation of chaos behaviour on damped and driven nonlinear simple pendulum motion simulated by mathematica

## Three nonlinear oscillators including restoring force, the simple pendulum motion, the cubic Duffing oscillator, the Sine-Gordon equation are offered to clarify the effectiveness and usefulness of the proposed technique. 提供了三个非线性振荡器，包括恢复力、单摆运动、三次 Duffing 振荡器、Sine-Gordon 方程，以阐明所提出技术的有效性和实用性。

The Rank Upgrading Technique for a Harmonic Restoring Force of Nonlinear Oscillators

10.1016/J.JOULE.2021.04.016

## Herein, we report an active resonance triboelectric nanogenerator (AR-TENG) system fabricated by using simple pendulum, tumbler, and flexible ring TENG, which can harvest omnidirectional and frequency varying water-wave energy through excellent structural design and resonance effect. 在此，我们报告了一种主动共振摩擦纳米发电机 (AR-TENG) 系统，该系统使用简单的摆锤、滚筒和柔性环 TENG 制造，该系统可以通过出色的结构设计和共振效果来收集全向和频率变化的水波能量。

Active resonance triboelectric nanogenerator for harvesting omnidirectional water-wave energy

10.1109/DDCLS52934.2021.9455503

## Numeral and simple pendulum examples examine the results and simulations show the effectiveness. 数字和简单的钟摆示例检查了结果，模拟显示了有效性。

A 2-Dimensional Linear Non-minimum Phase Estimator Based on Dynamic Exceeded Regressor

## We propose a simple pendulum model that accurately captures the velocity fluctuations of the particles in still fluid and find that differences in the falling style might be explained by a closer alignment between the particle's pitch angle and its velocity vector. 我们提出了一个简单的钟摆模型，可以准确地捕捉静止流体中粒子的速度波动，并发现下落方式的差异可以通过粒子的俯仰角与其速度矢量之间的更紧密对齐来解释。

Settling behaviour of thin curved particles in quiescent fluid and turbulence

10.1504/ijhvs.2021.10040934

## The testing rig is used to validate a simple pendulum-based, simplified three degree-of-freedom mathematical model of the response of a partially filled container to lateral accelerations. 该测试台用于验证一个简单的基于摆锤的简化三自由度数学模型，该模型是部分填充的容器对横向加速度的响应。

Experimental-theoretical modelling of the lateral sloshing in rail tankers

## Nondimensional equations are obtained by defining nondimensional parameters like; natural frequency, blade rotation, slenderness ratio, and simple pendulum frequency. 无量纲方程是通过定义无量纲参数获得的；固有频率、叶片旋转、长细比和单摆频率。

Parametric study of flapwise and edgewise vibration of horizontal axis wind turbine blades

## When expressed in elliptical coordinates the solution of the angular part is the same as the Schrödinger equation for the simple pendulum. 当用椭圆坐标表示时，角部分的解与单摆的薛定谔方程相同。

Pendulum beams: optical modes that simulate the quantum pendulum

10.1109/ICRA48506.2021.9561871

## A case study of applying LQR to a simple pendulum and simulations comparing the basins of attraction of minimal- and maximal-coordinate LQR controllers suggest that maximal-coordinate LQR achieves greater robustness and improved performance compared to minimal-coordinate LQR when applied to nonlinear systems. 将 LQR 应用于简单摆的案例研究以及比较最小和最大坐标 LQR 控制器的吸引力盆地的模拟表明，当应用于非线性系统时，与最小坐标 LQR 相比，最大坐标 LQR 实现了更大的鲁棒性和改进的性能。

Linear-Quadratic Optimal Control in Maximal Coordinates

10.1088/1742-6596/1936/1/012017

## In the first, simple SMS, such as the mass-spring system on a plane or the simple pendulum, are analysed. 首先，分析简单的 SMS，例如平面上的质量弹簧系统或简单的钟摆。

Interactive Mechanical Systems Using Mathematica

## However, systems examined to date have largely comprised simple pendulums limited to planar motion and to correspondingly limited degrees of excitational freedom. 然而，迄今为止检查的系统主要包括简单的钟摆，仅限于平面运动和相应的有限激发自由度。

The dynamics of an omnidirectional pendulum harvester

## In this paper, based on conventional photothermal shrinkable material or photothermal expansive material, a simple pendulum is proposed. 本文在传统的光热收缩材料或光热膨胀材料的基础上，提出了一种简单的摆锤。

Self-Sustained Oscillation of a Photothermal-Responsive Pendulum under Steady Illumination

## Tuning rules to achieve the desired settling time are explicitly derived and illustrated in an experimental study of a simple pendulum to track a reference trajectory with periodic velocity jumps. 在一个简单的钟摆的实验研究中明确推导出并说明了实现所需稳定时间的调整规则，以跟踪具有周期性速度跳跃的参考轨迹。

Prescribed-Time Stabilization of Controllable Planar Systems Using Switched State Feedback

10.1088/1742-6596/1811/1/012014

## This study aimed to investigate the chaos behavior resulted from damped driven nonlinear simple pendulum motion, which was simulated by using Mathematica. 本研究旨在研究由阻尼驱动的非线性单摆运动引起的混沌行为，该运动使用 Mathematica 进行模拟。

Investigation of chaos behaviour on damped and driven nonlinear simple pendulum motion simulated by mathematica

10.23919/ACC50511.2021.9483418

## A noticeable finding from the study of the necessary conditions is that the flight path angle of the optimal trajectory obeys the simple pendulum dynamics. 必要条件研究的一个显着发现是最优轨迹的航迹角服从简单的摆动力学。

Nonlinear Optimal Missile Guidance for Stationary Target Interception with Pendulum Motion Perspective

10.1109/AIIoT52608.2021.9454228

## To overcome the limitations of the high-order differential equations and the loop gain, the waveforms of the physical periodic motions are expressed by helix functions at time variation, and the characteristics of complex functions are used to examine the behaviors of the transmission spaces and the transmission networks in the different motion models including the Earth's motion, the simple pendulum systems, and the electronic systems. 为了克服高阶微分方程和环路增益的局限性，将物理周期运动的波形在时间变化时用螺旋函数表示，并利用复函数的特性来检验传输空间的行为和传输空间的行为。不同运动模型中的传输网络，包括地球运动、单摆系统和电子系统。

Study of Behaviors of Motion Models in High-Order Systems

## Contents Preface to the first edition xiii Preface to the second edition xvii 1 Differential and Difference Equations 1 10 Differential Equation Problems 1 100 Introduction to differential equations 1 101 The Kepler problem 4 102 A problem arising from the method of lines 7 103 The simple pendulum 10 104 A chemical kinetics problem 14 105 The Van der Pol equation and limit cycles 16 106 The Lotka-Volterra problem and periodic orbits 18 107 The Euler equations of rigid body rotation 20 11 Differential Equation Theory 22 110 Existence and uniqueness of solutions 22 111 Linear systems of differential equations 24 112 Stiff differential equations 26 12 Further Evolutionary Problems 28 120 Many-body gravitational problems 28 121 Delay problems and discontinuous solutions 31 122 Problems evolving on a sphere 32 123 Further Hamiltonian problems 34 124 Further differential-algebraic problems 36 13 Difference Equation Problems 38 130 Introduction to difference equations 38 131 A linear problem 38 132 The Fibonacci difference equation 40 133 Three quadratic problems 40 134 Iterative solutions of a polynomial equation 41 135 The arithmetic-geometric mean 43 CONTENTS 14 Difference Equation Theory 44 140 Linear difference equations 44 141 Constant coefficients 45 142 Powers of matrices 46 Numerical Differential Equation Methods 51 20 The Euler Method 51 200 Introduction to the Euler methods 51 201 Some numerical experiments 54 202 Calculations with stepsize control 58 203 Calculations with mildly stiff problems 60 204 Calculations with the implicit Euler method 63 21 Analysis of the Euler Method 65 210 Formulation of the Euler method 65 211 Local truncation error 66 212 Global truncation error 66 213 Convergence of the Euler method 68 214 Order of convergence 69 215 Asymptotic error formula 72 216 Stability characteristics 74 217 Local truncation error estimation 79 218 Rounding error 80 22 Generalizations of the Euler Method 85 220 Introduction 85 221 More computations in a step 86 222 Greater dependence on previous values 87 223 Use of higher derivatives 88 224 Multistep-multistage-multiderivative methods 90 225 Implicit methods 91 226 Local error estimates 91 23 Runge-Kutta Methods 93 230 Historical introduction 93 231 Second order methods 93 232 The coefficient tableau 94 233 Third order methods 95 234 Introduction to order conditions 95 235 Fourth order methods 98 236 Higher orders 99 237 Implicit Runge-Kutta methods 99 238 Stability characteristics 100 239 Numerical examples 103 CONTENTS vii 24 Linear Multistep Methods 105 …. 目录 第一版前言 xiii 第二版前言 xvii 1 微分方程和微分方程 1 10 微分方程问题 1 100 微分方程导论 1 101 开普勒问题 4 102 线法产生的问题 7 103 单摆 10 104 化学动力学问题 14 105 范德波尔方程和极限环 16 106 Lotka-Volterra 问题和周期轨道 18 107 刚体旋转的欧拉方程 20 11 微分方程理论 22 110 解的存在性和唯一性 22 111 线性系统微分方程组 24 112 刚性微分方程 26 12 进一步的演化问题 28 120 多体引力问题 28 121 延迟问题和不连续解 31 122 球面上演化的问题 32 123 进一步的哈密顿问题 34 124 进一步的微分代数问题 36 13 差分方程问题 38 130 差分方程简介 38 131 线性问题38 132 斐波那契差分方程 40 133 三个二次问题 40 134 多项式方程的迭代解 41 135 算术几何平均值 43 目录 14 差分方程理论 44 140 线性差分方程 44 141 常数系数 45 142 矩阵的幂 46 数值微分方程方法 51 20 欧拉方法 51 200 欧拉方法介绍 51 201 一些数值实验 54 202 使用步长控制的计算 58 203 具有轻度刚性问题的计算 60 204 使用隐式欧拉方法的计算 63 21 欧拉方法的分析 65 210欧拉方法 65 211 局部截断误差 66 212 全局截断误差 66 213 欧拉方法的收敛 68 214 收敛阶 69 215 渐近误差公式 72 216 稳定性特征 74 217 局部截断误差估计 79 218 舍入误差 80 22 欧拉的推广方法 85 220 简介 85 221 更多计算p 86 222 对先前值的依赖性更强 87 223 使用更高阶导数 88 224 多步-多级-多导数方法 90 225 隐式方法 91 226 局部误差估计 91 23 Runge-Kutta 方法 93 230 历史介绍 93 231 二阶方法 93 232 系数表格 94 233 三阶方法 95 234 阶条件介绍 95 235 四阶方法 98 236 高阶 99 237 隐式龙格-库塔方法 99 238 稳定性特征 100 239 数值示例 103 目录 vii 24 线性多步方法 105 ....

Numerical Methods for Ordinary Differential Equations

## We aim to develop a computer-based simple pendulum experiment set consisting of a simple pendulum, infrared phototransistor, and Arduino board for calculating the gravitational acceleration (g). 我们的目标是开发一个基于计算机的简单钟摆实验装置，由一个简单的钟摆、红外光电晶体管和 Arduino 板组成，用于计算重力加速度 (g)。

Development of a computer-based simple pendulum experiment set for teaching and learning physics

10.1007/978-981-15-9209-6_1

## The liquid free surface oscillation angle is simulated based upon the principles of the simple pendulum analogy for sloshing. 液体自由表面振荡角是根据简单摆类晃荡原理模拟的。

A Simplified Analytical Approach on the Dynamic Pressures in Cylindrical Vertical Tanks

## In this paper, a pendulum model is represented by a mechanical system that consists of a simple pendulum suspended on a spring, which is permitted oscillations in a plane. 在本文中，摆模型由一个机械系统表示，该系统由一个悬挂在弹簧上的简单摆组成，允许在平面内振荡。

A new pendulum motion with a suspended point near infinity

## For the period T(α) of a simple pendulum with the length L and the amplitude (the initial elongation) α ∈ (0, π), a strictly increasing sequence Tn(α) is constructed such that the relations T1(α)=2Lgπ−2+1ϵln1+ϵ1−ϵ+π4−23ϵ2,Tn+1(α)=Tn(α)+2Lgπwn+12−22n+3ϵ2n+2,$$\begin{array}{c} \displaystyle T_1(\alpha)=2\sqrt{\frac{L}{g}}\left[\pi-2+\frac{1}{\epsilon} \ln\left(\frac{1+\epsilon}{1-\epsilon}\right)+\left(\frac{\pi}{4}-\frac{2}{3}\right)\epsilon^2\right],\\ \displaystyle T_{n+1}(\alpha)=T_n(\alpha)+2\sqrt{\frac{L}{g}}\left(\pi w_{n+1}^2 - \frac{2}{2n+3}\right)\epsilon^{2n+2}, \end{array}$$ and 0<T(α)−Tn(α)T(α)<2ϵ2n+2π(2n+1),$$\begin{array}{} \displaystyle 0 \lt \frac{T(\alpha)-T_n(\alpha)}{T(\alpha)} \lt \frac{2\epsilon^{2n+2}}{\pi(2n+1)}\,, \end{array}$$ holds true, for α ∈ (0, π), n ∈ ℕ, wn:=∏k=1n2k−12k$\begin{array}{} \displaystyle w_n:=\prod_{k=1}^n\frac{2k-1}{2k} \end{array}$ (the nth Wallis’ ratio) and ϵ = sin(α/2). 对于长度为 L 和振幅（初始伸长）α ∈ (0, π) 的简单摆的周期 T(α)，构造严格递增的序列 Tn(α)，使得关系 T1(α)= 2Lgπ−2+1ϵln1+ϵ1−ϵ+π4−23ϵ2,Tn+1(α)=Tn(α)+2Lgπwn+12−22n+3ϵ2n+2,$$\begin{array}{c} \displaystyle T_1( \alpha)=2\sqrt{\frac{L}{g}}\left[\pi-2+\frac{1}{\epsilon} \ln\left(\frac{1+\epsilon}{1- \epsilon}\right)+\left(\frac{\pi}{4}-\frac{2}{3}\right)\epsilon^2\right],\\ \displaystyle T_{n+1}( \alpha)=T_n(\alpha)+2\sqrt{\frac{L}{g}}\left(\pi w_{n+1}^2 - \frac{2}{2n+3}\right) \epsilon^{2n+2}, \end{array}$$ 和 0<T(α)−Tn(α)T(α)<2ϵ2n+2π(2n+1),$$\begin{array}{ } \displaystyle 0 \lt \frac{T(\alpha)-T_n(\alpha)}{T(\alpha)} \lt \frac{2\epsilon^{2n+2}}{\pi(2n+1 )}\,, \end{array}$$ 成立，对于 α ∈ (0, π), n ∈ ℕ, wn:=∏k=1n2k−12k$\begin{array}{} \displaystyle w_n:= \prod_{k=1}^n\frac{2k-1}{2k} \end{array}$（第 n 个 Wallis 比率）和 ϵ = sin(α/2)。

How is the period of a simple pendulum growing with increasing amplitude?

10.1088/1757-899X/1188/1/012008

## The combination of the nonlinear rheological models to the simple pendulum in the conditions of the forced oscillations simulates the action of the let-off motion with weights. 非线性流变模型与单摆在强迫振荡条件下的结合模拟了带重物的送经运动。

Relaxation function experimental study of the warp strain at slow and regular weaving motion

10.22055/JACM.2020.35454.2660

## Three nonlinear oscillators including restoring force, the simple pendulum motion, the cubic Duffing oscillator, the Sine-Gordon equation are offered to clarify the effectiveness and usefulness of the proposed technique. 提供了三个非线性振荡器，包括恢复力、单摆运动、三次 Duffing 振荡器、Sine-Gordon 方程，以阐明所提出技术的有效性和实用性。

The Rank Upgrading Technique for a Harmonic Restoring Force of Nonlinear Oscillators

## The dynamic behaviors of the unperturbed system with irrational nonlinearity bear significant similarities to the coupling of a simple pendulum and the smooth and discontinuous (SD) oscillator with the coexistence of the standard homoclinic orbits of Duffing type and pendulum type and the coexistence of the nonstandard homoclinic orbits of SD type and pendulum type in the smooth and discontinuous case, respectively. 具有非理性非线性的未扰动系统的动力学行为与单摆和光滑不连续（SD）振荡器的耦合具有显着相似性，即标准的达芬型和摆型同宿轨道并存，非标准同宿轨道并存分别在光滑和不连续情况下的 SD 型和摆型轨道。

An approximate technique to test chaotic region in a rotating pendulum system with bistable characteristics

10.1088/1742-6596/1982/1/012146

## Compared with the common simple pendulum method and falling body method, the theoretical results show that our measurement method has higher precision and is feasible to accurately measure the acceleration of gravity. 与常见的单摆法和落体法相比，理论结果表明，我们的测量方法精度更高，准确测量重力加速度是可行的。

Systematic Research on Measuring Acceleration of Gravity by Laser Interferometry

## In particular, a number of classical non-linear oscillators, such as the simple pendulum model, the van der Pol circuital model and the Duffing oscillator class are recalled from the dedicated literature and are extended to evolve on manifold-type state spaces. 特别是，一些经典的非线性振荡器，如简单的钟摆模型、范德波尔电路模型和达芬振荡器类，从专门的文献中被召回，并被扩展为在流形类型的状态空间上演化。

Synthetic nonlinear second-order oscillators on Riemannian manifolds and their numerical simulation

## A nonlinear example of a simple pendulum also serves as a benchmark to illustrate the potential of the proposed approach. 一个简单摆的非线性示例也可以作为一个基准来说明所提出方法的潜力。

Uncertainty Quantification of Differential Algebraic Equations Using Polynomial Chaos

## The response of the nonlinear simple pendulum was used for benchmarking the boundary conditions for each of the four response regimes and the test criterion was demonstrated using relevant examples. 非线性单摆的响应用于对四种响应状态中的每一种的边界条件进行基准测试，并使用相关示例演示了测试标准。

Energy-Based Criterion for Testing the Nonlinear Response Strength of Strong Nonlinear Oscillators

10.35819/remat2021v7i1id4164

## In Physics, one of the applications is the simple pendulum that has oscillation independent of the mass, when it is constant. 在物理学中，应用之一是简单的钟摆，当它是恒定的时，它具有独立于质量的振荡。

Equações diferenciais aplicadas ao pêndulo com massa dependente do tempo: estudo de massa com variação exponencial e polinomial

10.1088/1742-6596/2049/1/012065

## This study aims to produce a digital simple pendulum prototype. 本研究旨在制作一个数字单摆原型。

Development of Digital Simple Pendulum Learning Media

## In this paper, a method to measure the gravitational acceleration by oscillation of a simple pendulum, using Arduino board, is presented. 在本文中，提出了一种使用 Arduino 板通过简单摆的振荡来测量重力加速度的方法。

Teaching Physics by Arduino during COVID-19 Pandemic: Oscillation of a simple pendulum

10.1016/j.ymssp.2020.107011

## The present study demonstrates how to perform a artificial intelligence assisted transport operation under variable conditions with hybrid control methods on a simple pendulum. 本研究展示了如何在简单摆锤上使用混合控制方法在可变条件下执行人工智能辅助运输操作。

An intelligent serial connected hybrid control method for gantry cranes

10.23919/ACC50511.2021.9483079

## Tuning rules to achieve the desired settling time are explicitly derived and illustrated in an experimental study of a simple pendulum to track a reference trajectory with periodic velocity jumps. 在一个简单的钟摆的实验研究中明确推导出并说明了实现所需稳定时间的调整规则，以跟踪具有周期性速度跳跃的参考轨迹。

Prescribed-Time Stabilization of Controllable Planar Systems Using Switched State Feedback

## vertically distributed mass), whereas broadleaves were better approximated by the simple pendulum model (i. 垂直分布的质量），而阔叶树更好 由简单的钟摆模型（i.

The motion of trees in the wind: a data synthesis

10.1007/978-3-030-75653-6_4

## The study of simple pendulum has a long history. 单摆的研究历史悠久。

Oscillations of a Pendulum Wrapping on Two Cylinders

10.1109/ICESC51422.2021.9532731

## To design the antenna, a simple pendulum shape structure is considered. 为了设计天线，考虑了一个简单的钟摆形状结构。

Design of Triple Band Slot Antenna for RF Energy Harvesting

10.1088/1742-6596/1806/1/012133

## The main purpose of this study is to figure out the effectivity of virtual laboratory on improving student’s conceptual understanding related to simple pendulum topic using PhET simulation. 本研究的主要目的是弄清楚虚拟实验室在使用 PhET 模拟提高学生对简单摆主题的概念理解方面的有效性。

Virtual experiment of simple pendulum to improve student’s conceptual understanding

## , a simple pendulum, is analyzed with a multiple scale method thanks to supposed assumptions about the excitation. ，一个简单的钟摆，由于对激励的假设假设，使用多尺度方法进行分析。

Nonlinear passive control of a pendulum submitted to base excitations

## More specifically, five basic structural models are considered: (a) the simple pendulum (SP), (b) the rigid inverted pendulum (RIP), (c) the flexural inverted pendulum (FIP), (d) the rigid rocking block (RRB), and (e) the flexural rocking block (FRB).

Revisiting the fundamental structural dynamic systems: the effect of low gravity

## In this paper, we present the dynamics of the simple pendulum by using the fractional-order derivatives.

Stability and Trajectories Analysis of a Fractional Generalization of Simple Pendulum Dynamic Equation

## We have considered two cases, a repulsive and attractive electric interactions as perturbations to the classical simple pendulum model.

Dynamics for an electric pendulum

## Such test was used to validate a simplified theoretical approach consisting of a two degree-of-freedom double pendulum mechanical system, where a simple pendulum, representing the sloshing cargo, is articulated to the spring-supported vehicle chassis, which is modelled as an inverted torsional pendulum.

Experimental Modeling of Railway Car Wheel-Forces During Turning

## The aim of this research is to develop teacher guidance material on 12th grade, in the subject of simple pendulum in physics lesson.

Development of teacher guide materials based on Logger Pro sensors for simple pendulum

10.1109/ISACS48493.2019.9068890

## In the first case, the main objective of the simple pendulum test is to determine the oscillation period (T), then the determination of the acceleration due by gravity (g).

Smartphones-based in educational practice works: a case study of mechanical vibration practical works

10.1016/j.heliyon.2019.e02827

## A laboratory activity based on the calculation of the oscillation period of a simple pendulum was done with 12 prospective teachers at the University of Extremadura, who were specializing in Biology/Geology, Physics/Chemistry, and Mathematics.

Improving the self-regulation in prospective science teachers: the case of the calculus of the period of a simple pendulum

## The setup is made up of a simple pendulum apparatus, an ultrasonic position sensor, and an Arduino Uno board.

Measurement of the gravitational acceleration using a simple pendulum apparatus, ultrasonic sensor, and Arduino

10.1016/J.CHAOS.2019.01.028

## In this paper, we introduce some practical applications of systems of FDAEs in physics such as a simple pendulum in a Newtonian fluid and electrical circuit containing a new practical element namely fractors.

System of fractional differential algebraic equations with applications

## The frequency of free oscillation of a damped simple pendulum with large amplitude depends on its amplitude unlike the amplitude-independent frequency of oscillation of a damped simple harmonic osc.

Free Oscillations of a Damped Simple Pendulum: An Analog Simulation Experiment

## To simulate the structural response to the bell ringing, the tower and the bell are modelled as a single degree of freedom system and an unforced and undamped simple pendulum, respectively.

Dynamic monitoring and evaluation of bell ringing effects for the structural assessment of a masonry bell tower

## It was found that for a simple pendulum, linearized equations were accurate for small values of θ and for damped oscillators, linearized equations were accurate after long time periods.

The nonlinear pendulum

## For the sake of simplicity, we model the swing by a simple pendulum, but allowing amplitudes beyond 90°.

Playground Physics: What Happens When Trying a 360° Swing?

## The Foucault pendulum is a simple pendulum basically set in a non-inertial reference frame.

Simulación numérica del péndulo de Foucault con Octave

## In this paper, two single-sided PTMDs (spring steel-type PTMD and simple pendulum-type PTMD) were designed and fabricated.

Experimental Study on Vibration Control of Suspended Piping System by Single-Sided Pounding Tuned Mass Damper

10.1080/0020739x.2019.1692934

## In differential equations textbooks, the motion of a simple pendulum for small-amplitude oscillations is analyzed.

Motion of a simple pendulum: a digital technology approach

## A simple pendulum is vertically excited on its support and consequently exhibiting oscillations and rotations.

Energy harvesting through pendulum motion and DC generators

## For instance, the smartphone-based acceleration sensor has been employed in a rather quick measurement of the acceleration due to gravity and in analyzing simple pendulum phenomena.

Measuring a spring constant with a smartphone magnetic field sensor

## In the field of physics teaching, the simple pendulum provides a very simple way to study the harmonic oscillator, the source of some fundamental concepts such as periodicity, relaxation time and anharmonicity.

A simple pendulum studied with a low-cost wireless acquisition board

## This paper proposes an analysis of walking balance in terms of movements of stance and swing legs based on an inverted pendulum and a simple pendulum.

Balance Map Analysis as a Measure of Walking Balance Based on Pendulum-Like Leg Movements

## e equilibrium position), similar to a simple pendulum.

Application of a two dipole model to PSR J1640-4631, a pulsar with an anomalous braking index.

10.1088/1742-6596/1286/1/012036

## Experiments with a damped simple pendulum were carried out and modelled for large amplitude motion with physics students in a mechanics laboratory course of the first year of the university.

Using a large amplitude pendulum in a learning cycle strategy

## It also finds applicability on the dynamics of the simple pendulum in a resistive medium.

Variational and Optimal Control Approaches for the Second-Order Herglotz Problem on Spheres

10.1088/1742-6596/1223/1/012004

## As the students have already known the kinematics, dynamics and energy analysis of a simple pendulum in harmonic case, we tried to find analogies between pendulum and compass.

From harmonic oscillation to chaotic motion of a compass

## As an example of the benefit of computer program in the classes room, the results of the comparison of the value of the gravitational acceleration from the data analysis with Tracker are presented; those results are compared to the value of the gravitational acceleration obtained during the development of traditional teaching experiments such as the simple pendulum.

Uso de Tracker para Análisis y Modelado de Datos Experimentales en Laboratorios Tradicionales de Fı́sica