DOING PHYSICS WITH MATLAB

WHATS NEW: Additions and Updates

• • VISUAL PHYSICS ONLINE: High School Physics Textbook Online – extensive use of Matlab for graphics and animations

• • Feb 2018 Satellite Motion GUI used for inputs. Finite difference method used to calculate a detailed description of the satellite motion

• • Feb 2018 Corrections to file cemVE08.m (corrections from Greg Robison, Hanover College)

• • new Feb 2018 FINITE DIFFERENCE METHOD: Analysis and design of ac ciruits without solving any differential equations. Can investigate circuits with non-sinusoidal input signals.

• • revised Jan 2018 ANIMATIONS: GIF and AVI FILES: [1D] Travelling Harmonic Transverse WaveJohn Sims     Biomedical Engineering Department, Universidade Federal do ABC, Brazil

• • revised Jan 2018 ANIMATIONS: GIF and AVI FILES: POLARIZED LIGHT: Linear, Circular, EllipticalJohn Sims     Biomedical Engineering Department, Universidade Federal do ABC, Brazil

• • Feb 2018 AC CIRCUIT ANALYSIS MADE SIMPE: Solving textbook problems with ease.

• • Feb 2018 Thermal Conduction: Temperature gradient and energy flux calculations through a composite rod

GETTING STARTED WITH MATLAB

• • Matlab Basics

• • XY Plots

• • Advanced XY plotting techniques

• • Creating a simple GUI with input boxes: SHM and the Sine Function

• • Creating and Saving Sounds: BEATS

DATA ANALYSIS and MATHEMATICAL ROUTINES

• • Curve Fitting: Least squares fit to a straight line for linear, power and exponential relationships

• • Curve Fitting: Weighted least squares fit for uncertainties in the y-data

• • Solving Quadratic Equations: GUI and Function call

• • Stationary Points of a function: Function to find the points of maximima and minima of a curve

• • VECTOR ANALYSIS: coordinates, vector algebra, dot product, cross product, [3D] rotation of axes

• • DIFFERENTIAL CALCULUS: 1st and 2nd derivatives; gradient; divergence; curl; Laplacian

• • INTEGRATION: Numerical computation of one-dimensional integrals

• • INTEGRATION: Estimate the value of the integral of the function y = f(x) between x = a and y = b

• • INTEGRATION: Numerical computation of two-dimensional integrals – double or surface integrals

• • SINC FUNCTION: Characteristics of the unnormalized sinc function

• • BESSEL FUNCTION OF THE FIRST KIND: Fraunhofer Diffraction from a circular aperture

• • SOLIDS OF REVOLUTION: [2D] and [3D] plots and an animation

• • Finite Difference Time Development Method: [1D] Scalar Wave Equation

• • PERCOLATION THEORY: A Matlab simulation of site percolation

MECHANICS / MECHANICAL SYSTEMS

• • Horizontal Motion with Resistance: drag and viscous drag force

• • Analytical and Numerical Analysis of Vertical Motion with Resistance: drag and viscous drag force, falling, drag coefficient

• • Animation of a vibrating spring: time variation of KE and PE

• • Animation of the Slingshot Effect

• • Physics of bungee jumps and bridge swings

• • Animation of the free fall vertical motion of an object: trajectory, displacement, velocity and acceleration time graphs

• • Satellite Motion GUI used for inputs. Finite difference method used to calculate a detailed description of the satellite motion

THERMAL PHYSICS

• • Thermal Conduction: Temperature gradient and energy flux calculations through a composite rod

• • Blackbody Radiation

• • Second Law of Thermodynamics – arrow of time: animation for the motion of gas molecules released from a corner of a room

• • Newton’s Law of Cooling: CSI Murder – time of death / Coffee cooling problem / First Order Differential Equations

ELECTROMAGNETISM           OPTICS           ELECTROMAGNETIC WAVES

• • HOME PAGE: Computational OPTICS and propagation of electromagnetic waves

• • Electric field and electric potential due to various charge distributions

• • Electric field and electric potential:     Line Integral of the electric field

• • Electric field and electric potential:     Method of Images

• • Electric field and electric potential:     Gauss’s Law and Electric Flux

• • Electrostatics:    Diververgence     /     Curl     /     Radial electric Fields

• • Numerical solution of [2D] Poisson’s and Laplace’s equations: introduction and examples

• • Numerical solution of [2D] Laplace’s equation: Two concentric conductive squares

• • Numerical solution of [2D] Poisson’s and Laplace’s equations: Examples using Dirchlet and Neumann boundary conditions

• • Animation: Electromagnetic Induction – induced current as magnet moves through a coil

• • Animation: DC Motor – Armature current, torque and rotation

• • Motion of charged particles through magnetic and electric fields: Numerical and graphical analysis

• • Electromagnetic Induction:    Faraday’s Law     /     Mutual Inductance     /     Self Inductance

• • Static Magnetic Fields:    Divergence     /     Curl     /     Biot-Savart Law

• • ANIMATIONS: GIF and AVI FILES: POLARIZED LIGHT: Linear, Circular, EllipticalJohn Sims     Biomedical Engineering Department, Universidade Federal do ABC, Brazil

OSCILLATIONS

• • Creating a simple GUI with input boxes: SHM and the Sine Function

• • Physics of bungee jumps and bridge swings

• • Forced vibration of a string: RESONANCE – animations of a vibrating string due a vibrator

WAVE MOTION

• • ANIMATIONS: GIF and AVI FILES: [1D] Travelling Harmonic Transverse WaveJohn Sims     Biomedical Engineering Department, Universidade Federal do ABC, Brazil

• • WAVE MOTION ANIMATED GIFS: Travelling, Transverse, Longitudinal Waves

• • BEATS: Superposition of two sinusoidal waves of slightly different frequencies: Creating and saving sounds

• • DOPPLER EFFECT: [2D] simulation for a moving source with sound effects and creation of animated gifs

• • Travelling waves along a string: Solving the wave equation for the transmission of energy along a string

• • Refraction: Animations of a plane wave incident upon an interface separating two different medium

• • Normal modes for air columns of varying cross-sectional area – musical instruments

• • Animated solutions of the [1D] Scalar Wave Equation using the Finite Difference Time Development Method

• • DIFFRACTION PHYICS: Single, Double, Particle with colour display corresponding with wavelength color

CIRCUITS

• • DC CIRCUITS:Voltage divider, Max power transfer, Wheatstone Bridge

• • Transient responses of RC circuits

• • ac Circuits: A complete analysis of ac circuits without the trogonometry and algebra.

• • RC FILTERS:: A complete analysis of low, high and band pass filters without all the messy algebra.

• • SERIES RESONANCE RLC series resonance circuit.An in-depth analysis of ac resonance circuits without all the algebra

• • PARALLEL RESONANCE RLC parallel voltage divider resonance circuit.An in-depth analysis of ac resonance circuits without all the algebra

• • AC CIRCUIT ANALYSIS MADE SIMPE: Solving textbook problems with ease.

• • FINITE DIFFERENCE METHOD: Analysis and design of ac ciruits without solving any differential equations.Can investigate circuits with non-sinusoidal input signals.

ATOMIC PHYSICS and QUANTUM PHYSICS

• • Millikan’s Oil Drop Experiment: Notes and Analysis of Experimental Data

• • Wave Particle Duality

• • Solving the time independent Schrodinger Equation for bound states using the finite difference method

• • Solving the time independent Schrodinger Equation for bound states using a matirx method for finding the eigenvalues and eigenvectors of the energy operator

• • Time evolution of the wavefunction – stationary and compound states

• • Hydrogen-like atoms and ions – solutions to the [3D] Schrodinger Equation

• • Hydrogen atom – transition rates, liftimes, selection rules, animations of compund states

• • Theory of alpha decay: Solving the Schrodinger Equation – tunnelling – half-life as a function of the energy of the alpha particle

• • Solving the [1D] time dependent Schrodinger equation with the Finite Difference Time Development method

BIOPHYSICS         NEUROSCIENCE

• • Transient responses of RC circuits

• • Hodgkin – Huxley Model: Membrane Current

• NEUROSCIENCE home page