Oscillator And Pendulum With A Random Mass

Oscillator And Pendulum With A Random Mass
Author: Moshe Gitterman
Publisher: World Scientific
Total Pages: 157
Release: 2015-01-05
Genre: Science
ISBN: 9814630764
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Stochastic descriptions of a harmonic oscillator can be obtained by adding additive noise, or/and three types of multiplicative noise: random frequency, random damping and random mass. The first three types of noise were intensively studied in many published articles. In this book the fourth case, that of random mass, is considered in the context of the harmonic oscillator and its immediate nonlinear generalization — the pendulum. To our knowledge it is the first book fully dedicated to this problem.Two interrelated methods, the Langevin equation and the Fokker-Planck equations, as well as the Lyapunov stability method are used for the mathematical analysis. After a short introduction, the two main parts of the book describe the different properties of the random harmonic oscillator and the random pendulum with random masses. As an example, the stochastic resonance is studied, where the noise plays an unusual role, increasing the applied weak periodic signal, and also the vibration resonance in dynamic systems, where the role of noise is played by the second high-frequency periodic signal.First and second averaged moments have been calculated for a system with different types of additive and multiplicative noises, which define the stability of a system. The calculations have been extended to two multiplicative noises and to quadratic noise. This book is useful for students and scientists working in different fields of statistical physics.

Noisy Oscillator, The: Random Mass, Frequency, Damping (2nd Edition)

Noisy Oscillator, The: Random Mass, Frequency, Damping (2nd Edition)
Author: Moshe Gitterman
Publisher: World Scientific Publishing Company
Total Pages: 189
Release: 2012-12-18
Genre: Science
ISBN: 9814440507
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The properties of the harmonic oscillator with random frequency or/and random damping formed the content of the first edition. The second edition includes hundreds of publications on this subject since 2005. The noisy oscillator continues to be the subject of intensive studies in physics, chemistry, biology, and social sciences.The new and the latest type of a stochastic oscillator has also been considered, namely, an oscillator with random mass. Such model describes, among other phenomena, Brownian motion with adhesion, where the molecules of the surrounding medium not only randomly collide, but also stick to the Brownian particle for some (random) time, thereby changing its mass. This edition contains two new chapters, eight new sections and an expanded bibliography. A wide group of researchers, students and teachers will benefit from this book.

Introduction to Oscillatory Motion With Mathematica

Introduction to Oscillatory Motion With Mathematica
Author: Steven Tan
Publisher: Lulu.com
Total Pages: 122
Release: 2016-09-14
Genre: Science
ISBN: 1365388123
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A survey of basic oscillatory concepts with the aid of Mathematica(R) computer algebra system to represent them and to calculate with them. It is written for students, teachers, and researchers needing to understand the basic of oscillatory motion or intending to use Mathematica(R) to extend their knowledge. All illustrations in the book can be replicated and used to learn and discover oscillatory motion in a new and exciting way. It is meant to complement the analytical skills and to use the computer to visualize the results and to develop a deeper intuitive understanding of oscillatory motion by observing the effects of varying the parameters of the problem.

The Nature of Code

The Nature of Code
Author: Daniel Shiffman
Publisher: No Starch Press
Total Pages: 642
Release: 2024-09-03
Genre: Computers
ISBN: 1718503717
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All aboard The Coding Train! This beginner-friendly creative coding tutorial is designed to grow your skills in a fun, hands-on way as you build simulations of real-world phenomena with “The Coding Train” YouTube star Daniel Shiffman. What if you could re-create the awe-inspiring flocking patterns of birds or the hypnotic dance of fireflies—with code? For over a decade, The Nature of Code has empowered countless readers to do just that, bridging the gap between creative expression and programming. This innovative guide by Daniel Shiffman, creator of the beloved Coding Train, welcomes budding and seasoned programmers alike into a world where code meets playful creativity. This JavaScript-based edition of Shiffman’s groundbreaking work gently unfolds the mysteries of the natural world, turning complex topics like genetic algorithms, physics-based simulations, and neural networks into accessible and visually stunning creations. Embark on this extraordinary adventure with projects involving: A physics engine: Simulate the push and pull of gravitational attraction. Flocking birds: Choreograph the mesmerizing dance of a flock. Branching trees: Grow lifelike and organic tree structures. Neural networks: Craft intelligent systems that learn and adapt. Cellular automata: Uncover the magic of self-organizing patterns. Evolutionary algorithms: Play witness to natural selection in your code. Shiffman’s work has transformed thousands of curious minds into creators, breaking down barriers between science, art, and technology, and inviting readers to see code not just as a tool for tasks but as a canvas for boundless creativity. Whether you’re deciphering the elegant patterns of natural phenomena or crafting your own digital ecosystems, Shiffman’s guidance is sure to inform and inspire. The Nature of Code is not just about coding; it’s about looking at the natural world in a new way and letting its wonders inspire your next creation. Dive in and discover the joy of turning code into art—all while mastering coding fundamentals along the way. NOTE: All examples are written with p5.js, a JavaScript library for creative coding, and are available on the book's website.

Noisy Oscillator, The: The First Hundred Years, From Einstein Until Now

Noisy Oscillator, The: The First Hundred Years, From Einstein Until Now
Author: Moshe Gitterman
Publisher: World Scientific
Total Pages: 159
Release: 2005-11-09
Genre: Science
ISBN: 9814479284
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This book contains comprehensive descriptions of stochastic processes described by underdamped and overdamped oscillator equations with additive and multiplicative random forcing. The latter is associated with random frequency or random damping. The coverage includes descriptions of various new phenomena discovered in the last hundred years since the explanation of Brownian motion by Einstein, Smoluchovski and Langevin, such as the shift of stable points, noise-enhanced stability, stochastic resonance, resonant activation, and stabilization of metastable states. In addition to many applications in physics, chemistry, biology, medicine, economics and sociology, these discoveries have clarified the deep relationship between determinism and stochasticity, which turns out to be complimentary rather than contradictory, with noise playing both constructive and destructive roles.

Galileo Unbound

Galileo Unbound
Author: David D. Nolte
Publisher: Oxford University Press
Total Pages: 384
Release: 2018-07-12
Genre: Science
ISBN: 0192528505
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Galileo Unbound traces the journey that brought us from Galileo's law of free fall to today's geneticists measuring evolutionary drift, entangled quantum particles moving among many worlds, and our lives as trajectories traversing a health space with thousands of dimensions. Remarkably, common themes persist that predict the evolution of species as readily as the orbits of planets or the collapse of stars into black holes. This book tells the history of spaces of expanding dimension and increasing abstraction and how they continue today to give new insight into the physics of complex systems. Galileo published the first modern law of motion, the Law of Fall, that was ideal and simple, laying the foundation upon which Newton built the first theory of dynamics. Early in the twentieth century, geometry became the cause of motion rather than the result when Einstein envisioned the fabric of space-time warped by mass and energy, forcing light rays to bend past the Sun. Possibly more radical was Feynman's dilemma of quantum particles taking all paths at once — setting the stage for the modern fields of quantum field theory and quantum computing. Yet as concepts of motion have evolved, one thing has remained constant, the need to track ever more complex changes and to capture their essence, to find patterns in the chaos as we try to predict and control our world.

Understanding Pendulums

Understanding Pendulums
Author: L.P. Pook
Publisher: Springer Science & Business Media
Total Pages: 145
Release: 2011-05-27
Genre: Technology & Engineering
ISBN: 9400714157
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Despite their apparent simplicity, the behaviour of pendulums can be remarkably complicated. Historically, pendulums for specific purposes have been developed using a combination of simplified theory and trial and error. There do not appear to be any introductory books on pendulums, written at an intermediate level, and covering a wide range of topics. This book aims to fill the gap. It is written for readers with some background in elementary geometry, algebra, trigonometry and calculus. Historical information, where available and useful for the understanding of various types of pendulum and their applications, is included. Perhaps the best known use of pendulums is as the basis of clocks in which a pendulum controls the rate at which the clock runs. Interest in theoretical and practical aspects of pendulums, as applied to clocks, goes back more than four centuries. The concept of simple pendulums, which are idealised versions of real pendulums is introduced. The application of pendulums to clocks is described, with detailed discussion of the effect of inevitable differences between real pendulums and simple pendulums. In a clock, the objective is to ensure that the pendulum controls the timekeeping. However, pendulums are sometimes driven, and how this affects their behaviour is described. Pendulums are sometimes used for occult purposes. It is possible to explain some apparently occult results by using modern pendulum theory. For example, why a ring suspended inside a wine glass, by a thread from a finger, eventually strikes the glass. Pendulums have a wide range of uses in scientific instruments, engineering, and entertainment. Some examples are given as case studies. Indexed in the Book Citation Index– Science (BKCI-S)

Understanding Acoustics

Understanding Acoustics
Author: Steven L. Garrett
Publisher: Springer
Total Pages: 913
Release: 2017-02-24
Genre: Science
ISBN: 3319499785
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This textbook provides a unified approach to acoustics and vibration suitable for use in advanced undergraduate and first-year graduate courses on vibration and fluids. The book includes thorough treatment of vibration of harmonic oscillators, coupled oscillators, isotropic elasticity, and waves in solids including the use of resonance techniques for determination of elastic moduli. Drawing on 35 years of experience teaching introductory graduate acoustics at the Naval Postgraduate School and Penn State, the author presents a hydrodynamic approach to the acoustics of sound in fluids that provides a uniform methodology for analysis of lumped-element systems and wave propagation that can incorporate attenuation mechanisms and complex media. This view provides a consistent and reliable approach that can be extended with confidence to more complex fluids and future applications. Understanding Acoustics opens with a mathematical introduction that includes graphing and statistical uncertainty, followed by five chapters on vibration and elastic waves that provide important results and highlight modern applications while introducing analytical techniques that are revisited in the study of waves in fluids covered in Part II. A unified approach to waves in fluids (i.e., liquids and gases) is based on a mastery of the hydrodynamic equations. Part III demonstrates extensions of this view to nonlinear acoustics. Engaging and practical, this book is a must-read for graduate students in acoustics and vibration as well as active researchers interested in a novel approach to the material.

The Noisy Oscillator

The Noisy Oscillator
Author: M. Gitterman
Publisher: World Scientific
Total Pages: 158
Release: 2005
Genre: Science
ISBN: 9812565124
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Stochastic Processes; Fluctuation Phenomena; Classical Statistical Mechanics; Oscillator; Brownian Motion; Stochastic Resonance; Multiplicative Noise.

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Publisher: IOS Press
Total Pages: 7289
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