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Numerical Calculation for Physics Laboratory Projects Using Microsoft EXCEL®

Shinil Cho

Description

This book may be used as a companion for introductory laboratory courses, as well as possible STEM projects. It covers essential Microsoft EXCEL® computational skills while analyzing introductory physics projects. Topics of numerical analysis include: multiple graphs on the same sheet, calculation of descriptive statistical parameters, a 3-point interpolation, the Euler and the Runge–Kutter methods to solve equations of motion, the Fourier transform to calculate the normal modes of a double pendulum, matrix calculations to solve coupled linear equations of a DC circuit, animation of waves and Lissajous figures, electric and magnetic field calculations from the Poisson equation and its 3D surface graphs, variational calculus such as Fermat's least traveling time principle, and the least action principle. Nelson's stochastic quantum dynamics is also introduced to draw quantum particle trajectories.

About Editors

Shinil Cho attended Rikkyo University in Tokyo for his BS, Seoul National University for his MS, and the Ohio State University for his PhD. He held postdoctoral fellowships at The Ohio State University and the University of Florida, in addition to a visiting professorship at the University of South Carolina. He has been at La Roche University since 1995, where he is currently an associate professor. His current research interests include quantum computation, biometrics, and physics education.

Table of Contents

1 Response time of nervous system

1.1          Objectives

EXCEL note

1.2 Theory and procedure

1.3 Data analysis

1.3.1 Histogram

1.3.2 Another histogram available in EXCEL

1.3.3 Statistical variables

1.3.4 Calculation of statistical variables

1.4 Central limit theorem

1.4.1 Gaussian curve fitting to raw data

1.4.2 Uniform distribution and the central limit theorem

References

 

2 Constant acceleration motion

2.1 Objectives

EXCEL note

2.2 Theory and procedure

2.3 Data analysis

2.3.1 Displacement vrs time graph

2.3.2 Displacement vrs time2 graph

2.3.3 Velocity vrs time graph

3 Equation of Motion

3.1 Objectives

EXCEL note

3.2 Theory and procedure

3.2.1 Projectile motion

3.3 Data analysis

3.4 Solving equation od motion using the Euler method

3.4.1 The Euler method for projectile motion

3.4.2 A falling object with air resistance using the Euler method

3.5 Rung-Kutter method

3.5.1 Limitation of the Euler method

3.5.2 Algorithm of the Runge-Kutter method

3.5.3 Harmonic oscillator

3.5.4 Van der Pool equation

3.6 Runge-Kutter method for simultaneous ordinary differential equations

3.6.1 Algorithm

3.6.2 Planetary motion

References

 

4 Periodic motions

4.1 Objectives

EXCEL note

4.2 Theory and Procedure

4.3 Data analysis

4.4 Further investigation – minimum period of a physical pendulum

4.5 More periodic motions

4.5.1 Double pendulum

4.5.2 Fourier transform

4.5.3 Coupled Oscillators

References

 

5 Lissajous Figures

5.1 Objectives

EXCEL note

5.2 Theory and procedure

5.3 Lissajous figures using EXCEL

5.4 Animation of graphs

5.4.1 Idea of animating EXCEL chart

                5.4.2 A propagating sine-wave

5.4.3 Rotating Lissajous figures

References

 

6 Kirchhoff's law

6.1 Objectives

EXCEL note

6.2 Theory and procedure

6.3 Circuit under measurement

6.3.1 Matrix calculation using EXCEL

6.4 Data analysis

 

7 Equipotential surface

7.1 Objectives

EXCEL note

7.2 Measurement

7.3 Data Analysis

7.3.1 3D Surface Graph

7.3.2 Calculation of 3D equipotential surface of an electric dipole

7.4 Further investigation

7.4.1 Two-dimensional electric potential from Poisson equation

7.4.2 Two-dimensional electric field from electric potential

7.4.3 Spreadsheet for calculating electric dipole field

7.4.4 Graphical representation of electric field

References

 

8 Magnetic field profile

8.1 Objectives

EXCEL note

8.2 Theory and Procedure

8.3 Measurement

8.4 Additional study

8.4.1 Magnetic field calculated from vector potential

8.4.2 Vector potential and magnetic field due to a pair of current wire

8.4.3 Graphical representation of the magnetic field from a pair of current wires

References

 

9 Law of refraction

9.1 Objectives

EXCEL note

9.2 Theory and procedure

9.3 Data analysis

9.3.1 Angle measurement

9.3.2 Fermat's least traveling principle using EXCLE's Solver

9.4 Projectile motion based on the least action principle

9.4.1 Lagrangian approach

9.4.2 Projectile motion

9.5 Eigen value problems using Solver

9.5.1 Eigenvalues of Strum-Liouville equation

9.5.2 Example

References

 

10 Quantum particle trajectories

10.1 Objectives

EXCEL note

10.2 Theory – Nelson's approach

10.3 Analysis of quantum particle trajectories

10.3.1 One-dimensional free particle

10.3.2 One-dimensional potential barrier

10.3.3 Harmonic oscillator

10.3.4 Hydrogen atom

References

 

Appendix

A1. EXCEL options

A1.1 Autofill

A1.2 Adding "Data Analysis"

A1.3 Enabling VBA macro

A1.4 Recording macro code

A1.5 Enabling iterative calculation

A1.6 Generating Gaussian random numbers

A2. Calculation of firing speed of a rolling ball

A3. RLC oscillator circuit

A4. Another circuit for exercising Kirchhoff's law

A5. Macro codes for quantum particles

References

Bibliographic

Paperback ISBN: 9780750330138

Ebook ISBN: 9781643277257

DOI: 10.1088/2053-2571/ab318f

Publisher: Morgan & Claypool Publishers

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