Period Of Pendulum Research Articles

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.

Coriolis acceleration and critical slowing-down: A quantitative laboratory experiment

We experimentally investigate the motion of a pendulum on a turntable. The dynamics of this conical pendulum experiment are very rich and can be studied both at the undergraduate and graduate levels. At low rotational frequency of the turntable, we measure the Coriolis acceleration. Increasing the rotational frequency, we experimentally demonstrate a supercritical pitchfork bifurcation: above a critical rotational frequency, the pendulum arm spontaneously rises up. Beyond the characterization of the equilibrium pendulum angle, we evidence the so-called critical slowing down corresponding to the increase in the pendulum period when approaching the critical rotational frequency. Bifurcation and critical slowing down are key concepts in the study of critical phenomena that are seldom illustrated experimentally. All our experimental measurements are in excellent quantitative agreement with the theory we provide.

Exact and Approximate Formulae for the Period of Simple Pendulum

Pendulum plays a significant role in certain practical aspects such as measuring gravitational acceleration and proving the rotation of Earth. In traditional textbooks, only a simplified approximate formula for calculating pendulum period in small angle is given. As a matter of fact, the analytical derivation of the pendulum period can always be given in the form of elliptical integral simply using the law of the conservation of energy. The form, however, is relatively complex for students and beginners in physics. Thus, a simplified version of the period of simple pendulum is highly desirable. This article is going to present a series of approximate formulae for pendulum period and conduct some comparison among these different formulae. This essay is dedicated to help readers and beginners in physics to look into the process of deriving the pendulum period formula, and also provide a convenient way for readers to look up certain literatures in this research area.

CDIO‐CT collaborative strategy for solving complex STEM problems in system modeling and simulation: An illustration of solving the period of mathematical pendulum

AbstractThe problem‐project‐oriented STEM education plays a significant role in training students' ability of innovation. Although the conceive‐design‐implement‐operate (CDIO) approach and computational thinking (CT) are hot topics in recent decades, there are still two deficiencies: the CDIO approach and CT are discussed separately and a general framework of coping with complex STEM problems in system modeling and simulation is missing. In this paper, a collaborative strategy based on the CDIO and CT is proposed for solving complex STEM problems in system modeling and simulation with a general framework, in which the CDIO is about “how to do,” CT is about “how to think,” and the project means “what to do.” As an illustration, the problem of solving the period of mathematical pendulum is discussed in detail. The most challenging task involved in the problem is to compute the complete elliptic integral of the first kind (CEI‐1). In the philosophy of STEM education, all problems have more than one solution. For computing the CEI‐1, four methods are discussed with a top‐down strategy, which includes the infinite series method, arithmetic‐geometric mean method, Gauss–Chebyshev method, and Gauss‐Legendre method. The algorithms involved can be utilized for R & D projects of interest and be reused according to the requirements encountered. The general framework for solving complex STEM problems in system modeling and simulation is worth recommending to college students and instructors.

Semiclassical calculation of the pendulum period

Abstract In this paper, we calculate the swing period of the classical pendulum via semiclassical path-integration. We point out the significance of the classical periodic orbits and the equivalence of pendulum’s classical isochronism to the equidistance of the quantum energy levels. We derive the swing period in terms of the semiclassical tunneling time and the fractional revival period. A possible definition of a critical value for the quantum ‘bounce time’ is proposed. This paper intends for graduate students as an illustrating example of applying quantum mechanics to a classical system. It offers valuable insight into some characteristics that the classical and quantum pendulum possess in common. It also intends for a specialist in quantum chemistry where the quantum pendulum dynamics appears in what is known as hindered rotation about some chemical bonds.

Computing the gravitational acceleration within the World Pendulum Alliance as an application of the remote laboratory methodology

This paper describes a method for calculating gravitational acceleration using simple pendulums available through the World Pendulum Alliance. This network comprises fourteen institutions across eight countries, each providing a pendulum that can be accessed remotely via the Internet. We demonstrate how to measure the pendulum's period for N oscillations, discussing the importance of repetitions and samples in minimizing experimental uncertainty. We then use the averaged period value to compute the local gravitational acceleration, accounting for corrections due to the moment of inertia of the system. Finally, we analyze the geographical location of each pendulum to explore the dependence of gravity on latitude, longitude, and altitude and discuss its implications for the Earth's shape. We believe this tool will be useful for physics courses at the introductory and university levels due to its remote access features and its relevance to fundamental concepts.

The Relationship between Air Resistance and the Vibrating Period of Simple Pendulum

The simple pendulum is a typical model of the compound pendulum. In this model, resistance and buoyancy are negligible. This paper researches how air resistance affects the vibration period in the simple pendulum model but with exact conditions. There are two simplified air resistance models that can apply in the models, one is the first power air resistance model, and the second is the second power air resistance model. But the first power air resistance model is quite complex, there is no equipment to measure its coefficient of it, so it only applies the second power air resistance. This paper studies the formula that revealed air resistance and related suitable cases. The results show that the time from the formula is longer than the experiment a little bit.

Problem in Deriving the Period of Simple Pendulum in Physics Textbooks and Proposal for Solution

Problem in Deriving the Period of Simple Pendulum in Physics Textbooks and Proposal for Solution

Analyzing compound pendulum data

The period T of an undamped compound pendulum depends on just three variables, the rotation axis to center of mass distance a, the gyradius k of the pendulum about its center of mass and the gravitational acceleration g. The extraction of these parameters from typical undergraduate measurements of the pendulum period as a function of the axis position x is presented. Measurement of just two periods and the pivot displacement Δx allows any two of the parameters to be measured. Three period measurements at pivot displacements b and c allow all three parameters a, k and g to be determined, without any knowledge of the pendulum properties.

Decayless longitudinal oscillations of a solar filament maintained by quasi-periodic jets

Context. As a ubiquitous phenomenon, large-amplitude longitudinal filament oscillations usually decay in 1–4 periods. Recently, we observed a decayless case of such oscillations in the corona. Aims. We try to understand the physical process that maintains the decayless oscillation of the filament. Methods. Multiwavelength imaging observations and magnetograms were collected to study the dynamics of the filament oscillation and its associated phenomena. To explain the decayless oscillations, we also performed one-dimensional hydrodynamic numerical simulations using the code MPI-AMRVAC. Results. In observations, the filament oscillates without decay with a period of 36.4 ± 0.3 min for almost 4 h before eruption. During oscillations, four quasi-periodic jets emanate from a magnetic cancellation site near the filament. The time interval between neighboring jets is ∼68.9 ± 1.0 min. Numerical simulations constrained by the observations reproduced the decayless longitudinal oscillations. However, it is surprising to find that the period of the decayless oscillations is not consistent with the pendulum model. Conclusions. We propose that the decayless longitudinal oscillations of the filament are maintained by quasi-periodic jets, which is verified by the hydrodynamic simulations. More importantly, it is found that, when it is driven by quasi-periodic jets, the period of the filament longitudinal oscillations also depends on the driving period of the jets, not on the pendulum period alone. With a parameter survey in simulations, we derived a formula by which the pendulum oscillation period can be derived using the observed period of decayless filament oscillations and the driving periods of jets.

Hubungan Antara Variasi Sudut dengan Nilai Periode pada Bandul Menggunakan Mikrokontroller Arduino

Pendulum motion is an example of simple harmonic motion which undergoes back and forth motion through its equilibrium point regularly. In the motion of a pendulum there is a period which is the time it takes to travel one path of the pendulum. In determining the period of the pendulum, there are quantities that affect the period of the pendulum, one of which is the initial deviation. This study aims to prove and determine the relationship between the magnitude of the pendulum deviation with the value of the pendulum period. The value of the period of the pendulum at an angle of <10 0 will be different from the value of the period at an angle of >10 0 . Experiments were carried out using Arduino as a digital practicum tool, this is because the digital practicum tool has a high accuracy value and has a low relative error. The angle variations selected are 10 0 , 20 0 , 30 0 , and 40 0 , the results obtained in the experiment show that there is a significant difference between the coefficient of variation of the pendulum and the coefficient of the pendulum period.

Why do we choose the fastest point as a reference to measure the simple pendulum period by a stopwatch?

Since the vibration of a single pendulum is very periodic, measuring its period is a very interesting topic. When students are asked to measure the period of a single vibration, they start and stop the stopwatch when the pendulum reaches the top point as a reference point. In this paper, we try to show that the error can be reduced more by using the equilibrium point, that is, the bottom position as the reference rather than the top position. We think it would be beneficial for students to measure the period in both cases, compare the errors, and think about the reasons for error differences. Students believe that the moment the pendulum moved slowly and nearly stopped at the top was more likely to measure the time to be more accurate. The reason for this is that they think the pendulum will move so fast when it passes the bottom point that they will not be able to start or stop the stopwatch accurately at the instant passing the lowest point. We are also able to obtain the error of the position measurement by using the recorded video of a simple pendulum.

A Forgotten Simple Pendulum Period Equation

The variation of the period of oscillation of a pendulum with the amplitude is known as “circular error” to clockmakers, and can easily be observed even without modern laboratory instruments. There have therefore been many approximate formulae for the pendulum period as a function of the amplitude, but the simple equation due to Denman, TD(φ0)=T0/(1−φ02/16),(1)which is more accurate than many in the literature, seems to have been forgotten.

Review of approximate equations for the pendulum period

Precision measurements of the pendulum period as a function of the amplitude can now be made with a variety of instruments including MEMs gyro/accelerometers, and thus theoretical expressions are required for comparison. Unfortunately exact solution of the pendulum equation involves elliptic integrals, which cannot be expressed in terms of elementary functions, and therefore a wide variety of approximations have been published. These range from simple single-term formulae to more sophisticated equations, which apply to a wider range of amplitudes, to an iterative procedure for calculating the precise period. The published approximations are compared as Taylor series expansions, and graphically to indicate their accuracy and their regions of applicability.

A viabilidade do uso do pêndulo simples como ferramenta no ensino de física do ensino médio para o cálculo da aceleração da gravidade local

Knowing the g-value of acceleration of gravity is of paramount importance in various analyzes, and there are several ways of obtaining it experimentally. Here, searching for resources that are easy to apply in high school classrooms, the authors opted for the observation of a simple pendulum, performing a series of measurements of the pendulum period and applying them to the equations (appropriately manipulated for this experiment) of this oscillatory movement. The experiment was carried out in four steps: one with a mass of 10 grams and three with a mass of 20 grams; two with ten swings, one with fifteen and one with twenty. As a result, four values of local acceleration were estimated,which were compared, using the theory of errors, with the value made available in the literature. With these data, the feasibility of using this device in the teaching-learning process was verified, given its ease of handling and assembly, its low cost and its negligible error with the value of the literature.

Numerical solution for time period of simple pendulum with large angle

In this study, the numerical solution of the ordinary kind of differential equation for a simple pendulum with large-angle of oscillation was introduced to obtain the time period. The analytical solution is obtained in terms of elliptic functions, and numerical solution of the problem was achieved by using two numerical quadrature methods, namely, Simpson?s 3/8 and Boole?s method. The period of a simple pendulum with large angle is presented. A comparison has been carried out between the analytical solution and the numerical integration results. In the case of error analysis, absolute and relative errors of the problem have been presented. A numerical algorithm has been developed by MATLAB software 2013R and used for analyzing the result. It is established that the results of the comparison guaranty the ability and the accuracy of the present method.

Approximate period for large-amplitude oscillations of a simple pendulum based on quintication of the restoring force

A new approximate formula for estimating the period of the simple pendulum has been presented in this paper. The formula was derived based on ‘quintication’ of the restoring force of the pendulum, which replaces the original pendulum equation with an equivalent cubic–quintic oscillator. The coefficients of the equivalent oscillator are amplitude-dependent and were derived based on quasi-static equilibrium principles. Then, an approximate solution for the equivalent cubic–quintic oscillator was applied to derive the approximate formula used to estimate the pendulum period for the entire range of possible amplitudes of angular displacement, i.e. The formula is simple and very accurate with a maximum relative error of 0.421% for amplitudes up to 179.9°.

Testing the generalized uncertainty principle with macroscopic mechanical oscillators and pendulums

Recent progress in observing and manipulating mechanical oscillators at quantum regime provides new opportunities of studying fundamental physics, for example, to search for low energy signatures of quantum gravity. For example, it was recently proposed that such devices can be used to test quantum gravity effects, by detecting the change in the [x,p] commutation relation that could result from quantum gravity corrections. We show that such a correction results in a dependence of a resonant frequency of a mechanical oscillator on its amplitude, which is known as amplitude-frequency effect. By implementing this new method we measure amplitude-frequency effect for 0.3 kg ultra high-Q sapphire split-bar mechanical resonator and for 10 mg quartz bulk acoustic wave resonator. Our experiments with sapphire resonator have established the upper limit on quantum gravity correction constant for $\beta_0<5 \times10^6$ which is a factor of 6 better than previously detected. The reasonable estimates of $\beta_0$ from experiments with quartz resonators yield an even more stringent limit of $4\times10^4$. The data sets of 1936 measurement of physical pendulum period by Atkinson results in significantly stronger limitations on $\beta_0 \ll 1$. Yet, due to the lack of proper pendulum frequency stability measurement in these experiments, the exact upper bound on $\beta_0$ can not be reliably established. Moreover, pendulum based systems only allow testing a specific form of the modified commutator that depends on the mean value of momentum. The electro-mechanical oscillators to the contrary enable testing of any form of generalized uncertainty principle directly due to much higher stability and a higher degree of control.

Pythagorean triangles analysis of the conical pendulum based on lengths, forces and times, to obtain equations for the principal physical parameters

An original approach using three appropriate Pythagorean triangles is presented for the detailed mathematical analysis of an ideal conical pendulum. The triangles that are used in this analysis relate specifically to the physical dimensions of the conical pendulum, the magnitudes of the forces acting during the conical pendulum motion and a triangular construction involving the conical pendulum period. It is assumed that known values for the conical pendulum mass, local value for the acceleration due to gravity and the conical pendulum string length are readily available. The following physical parameters can then be calculated directly from accurate experimental measurements of the conical pendulum period only: string tension force, centripetal force (and consequently the centripetal acceleration), orbital radius, orbital speed, apex angle, magnitude of the angular momentum, potential and kinetic energies. The analysis concludes with the very straightforward derivation of a well-known simple trigonometric identity, which serves to support the internal self-consistency of the Pythagorean triangles technique that is presented here.

Magnetic monitoring of a small Foucault pendulum.

A three-axis magnetometer is used to measure the precession angle of a small Foucault pendulum of 65.4 cm length and period 1.623 s. The swinging brass bob (4 kg) contains a small neodymium magnet to detect and sustain its motion. A microcontroller is used to control electronics that drive the pendulum while sampling the time-dependent magnetic field from the swinging bob. These data are used to calculate the precession angle for each pendulum period. Long-term studies demonstrated a precession rate of 10.31°/h which is within 0.5% of that expected for the latitude of the experiment. Considerable short-term variation in the precession rate is observed (1.5°/h) which is correlated with the structure of the pendulum mechanics. The angle measurement noise is found to be 0.059° which enables a clear detection of the earth's rotation with only 26.7 s of observation.