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Numerical Exploration of Fourier Transform and Fourier Series

The Power Spectrum of Driven Damped Oscillators

Abdullah Al Sakib, Sujaul Chowdhury

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Springer Nature Switzerland img Link Publisher

Naturwissenschaften, Medizin, Informatik, Technik / Theoretische Physik

Beschreibung

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

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Schlagwörter

Numerics, 4th Order Runge-Kutta Method, Discrete Fourier Transform, Fourier Transform, Mathematica, Fourier Series, Phase Space, Power Spectrum, Driven Damped Oscillators