1st Edition
Simulations of Oscillatory Systems with Award-Winning Software, Physics of Oscillations
Deepen Your Students’ Understanding of Oscillations through Interactive Experiments
Simulations of Oscillatory Systems: with Award-Winning Software, Physics of Oscillations provides a hands-on way of visualizing and understanding the fundamental concepts of the physics of oscillations. Both the textbook and software are designed as exploration-oriented supplements for courses in general physics and the theory of oscillations.
The book is conveniently structured according to mathematical complexity. Each chapter in Part I contains activities, questions, exercises, and problems of varying levels of difficulty, from straightforward to quite challenging. Part II presents more sophisticated, highly mathematical material that delves into the serious theoretical background for the computer-aided study of oscillations.
The software package allows students to observe the motion of linear and nonlinear mechanical oscillatory systems and to obtain plots of the variables that describe the systems along with phase diagrams and plots of energy transformations. These computer simulations provide clear, vivid illustrations of oscillations in various physical systems, bringing to life many abstract concepts, developing students’ physical intuition, and complementing the analytical study of the subject. Students can investigate phenomena that would otherwise be difficult to study in a more conventional manner.
Introduction
Oscillations in Simple Systems
Free Oscillations of a Linear Oscillator
Summary of the Theory
Review of the Principal Formulas
Questions, Problems, Suggestions
Torsion Spring Oscillator with Dry Friction
Summary of the Theory
Review of the Principal Formulas
Questions, Problems, Suggestions
Forced Oscillations in a Linear System
Summary of the Theory
Steady-State Forced Oscillations
Transient Processes
Review of the Principal Formulas
Questions, Problems, Suggestions
Square-Wave Excitation of a Linear Oscillator
Theoretical Background
Steady-State Forced Oscillations under the Square-Wave Torque
Transient Processes under the Square-Wave External Torque
Estimation of the Amplitude of Steady-State Oscillations
Energy Transformations
The Electromagnetic Analogue of the Mechanical System
Concluding Remarks
Review of the Principal Formulas
Questions, Problems, Suggestions
Parametric Excitation of Oscillations
Summary of the Theory. General Concepts
Frequency Ranges of Parametric Excitation
Concluding Remarks
Questions, Problems, Suggestions
Sinusoidal Modulation of the Parameter
Summary of the Theory: Basic Concepts
The Intervals of Parametric Instability
Concluding Remarks
Questions, Problems, Suggestions
Nonlinear Oscillations
Free Oscillations of the Rigid Pendulum
Summary of the Theory
Oscillations of the Pendulum with Extremely Large Amplitudes
Period of Revolutions and Large Oscillations
The Influence of Friction
Review of the Principal Formulas
Questions, Problems, Suggestions
Rigid Planar Pendulum under Sinusoidal Forcing
Regular Response of a Harmonically Driven Rigid Pendulum
Steady-State Response-Frequency Curves
Subharmonic and Superharmonic Resonances
Other Extraordinary Regular Forced Oscillations
Concluding Remarks
Pendulum with a Square-Wave Modulated Length
The Investigated Physical System
The Threshold of Parametric Excitation
Autoresonance, Bifurcations, Multistability
Quantitative Theory of Parametric Excitation
Frequency Ranges for Parametric Resonance
Intervals of Parametric Excitation in the Presence of Friction
Concluding Remarks
Rigid Pendulum with Oscillating Pivot
Introductory Notes
Kapitza’s Pendulum— Dynamic Stabilization
The Physical Model of the Investigated System
Parametric Resonance
Physical Reasons for Stability of the Inverted Pendulum
An Approximate Quantitative Theory of the Inverted Pendulum
Exact Differential Equation for Pendulum with Oscillating Pivot
Effective Potential Function for a Pendulum
Subharmonic Resonances of High Orders
Upper Boundary of Dynamic Stability
Enhanced Criterion for Kapitza’s Pendulum Stability
Complicated Regular Motions of the Parametrically Driven Pendulum
Chaotic Motions of the Pendulum
Concluding Remarks
Torsion Pendulum with Dry and Viscous Damping
Basics of the Theory
Sinusoidally Driven Oscillator with Dry Friction
Excitation at Sub-Resonant Frequencies
Concluding Remarks
Bibliography
Index
Biography
Eugene I. Butikov is a professor of physics at St. Petersburg State University. His work focuses on solid-state physics and the theory of nonlinear oscillations as well as developing interactive educational software for university-level physics students.
"... provides a hands-on way of visualizing and understanding the fundamental concepts of the physics of oscillations. ... conveniently structured according to mathematical complexity. Each chapter in Part I contains activities, questions, exercises, and problems of varying levels of difficulty, from straightforward to quite challenging. Part II presents more sophisticated, highly mathematical material that delves into the serious theoretical background for the computer-aided study of oscillations. The software package allows students to observe the motion of linear and nonlinear mechanical oscillatory systems and to obtain plots of the variables that describe the systems along with phase diagrams and plots of energy transformations. These computer simulations provide clear, vivid illustrations of oscillations in various physical systems, bringing to life many abstract concepts, developing students' physical intuition, and complementing the analytical study of the subject. Students can investigate phenomena that would otherwise be difficult to study in a more conventional manner. Exceptionally well written, organized and presented ... an ideal textbook for university-level physics curriculums and academic library reference collections."
—Midwest Book Review, April 2015
