Numerical Exploration of Fourier Transform and Fourier Series: The Power Spectrum of Driven Damped Oscillators

by Sujaul Chowdhury, Abdullah Al Sakib

Overview

This book presents practical demonstrations of numerically calculating or obtaining Fourier Transform. In particular, the authors demonstrate how to obtain frequencies that are present in numerical data and utilizes Mathematica to illustrate the calculations. This book also contains numerical solution of differential equation of driven damped oscillator using 4th order Runge-Kutta method. Numerical solutions are compared with analytical solutions, and the behaviors of mechanical system are also depicted by plotting velocity versus displacement rather than displaying displacement as a function of time.  This book is useful to physical science and engineering professionals who often need to obtain frequencies present in numerical data using the discrete Fourier transform.

This book:

• Aids readers to numerically calculate or obtain frequencies that are present in numerical data
• Explores the use of the discrete Fourier transform and demonstrates practical numerical calculation
• Utilizes 4th order Runge-Kutta method and Mathematica for the numerical solution of differential equation

Product Details

ISBN-13:	9783031346644
Publisher:	Springer-Verlag New York, LLC
Publication date:	08/01/2023
Series:	Synthesis Lectures on Mathematics & Statistics
Sold by:	Barnes & Noble
Format:	eBook
File size:	13 MB
Note:	This product may take a few minutes to download.

About the Author

Sujaul Chowdhury, Ph.D., is a Professor in Department of Physics at Shahjalal University of Science and Technology. He also received his B.Sc. and M.Sc. in Physics from Shahjalal University of Science and Technology, before earning his Ph.D. at The University of Glasgow. After completing his Ph.D., Dr. Chowdhury was a Humboldt Research Fellow for one year at The Max Planck Institute. He is the author of many books, including Monte Carlo Methods: A Hands-On Computational Introduction Utilizing Excel and Monte Carlo Methods Utilizing Mathematica®: Applications in Inverse Transform and Acceptance-Rejection Sampling, which are  also in the Synthesis Lectures on Mathematics&Statistics series published by Springer Nature. His research interests include nanoelectronics, magnetotransport in semiconductor nanostructures, and nanostructure physics.

Abdullah Al Sakib is an M.S. student in the Department of Physics at Shahjalal University of Science and Technology.

Table of Contents

Exploring Fourier Transform and Fourier Series Approximation Numerically.- Motion and Power Spectrum of Driven Damped Oscillators, Analytical and Numerical Accounts.- Motion of Driven Damped Oscillators in Phase Space. References.