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Mathematica examples from the LC undergraduate physics curriculum. John Eric Goff Lynchburg College Lynchburg, VA 24501. CS-AAPT Fall 2007 – Radford University Radford, VA 24142. November 3, 2007. LC Physics.

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## Mathematica examples from the LC undergraduate physics curriculum

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**Mathematica examples from the LC undergraduate physics**curriculum John Eric Goff Lynchburg College Lynchburg, VA 24501 CS-AAPT Fall 2007 – Radford University Radford, VA 24142 November 3, 2007**LC Physics**• Small number of physics faculty (2 or 3). • We need a niche! • We have a computational emphasis. • Computational Physics joins theory and experiment to form the new triumvirate in physics. • Some form of computation permeates all our courses.**What do we do?**• Intro: Excel (Euler method in second lab), some Mathematica, simulations (Kinetic Books and Physlets) • Intermediate: Mathematica (especially Classical Mechanics in 4th semester) • Advanced: Mathematica and Full Programming (Computational Physics Course)**Intro Example (1st Semester)**• “Curtain of Death” problem (HRW 4-68)**What is typically done?**Excel Plot**Intro Lab – Kirchhoff’s Rules**PASCO Six equations in six unknowns (currents)! How do students compare with theory without spending most of “lab” doing algebra???**Use Mathematica!**• Make sure students write down the six equations in six unknowns. Do not skip the physics! Students evaluate “sol” with their own V and R values.**Classical Mechanics**• Taken by sophomores in spring semester. • Mathematica is used throughout course. • One week of class devoted to Mathematica. • Homework and exam questions require numerical solutions.**Velocity-Dependent Forces**• Thornton and Marion 2-18 (worked fully in class) • Softball problem uses quadratic air drag. • Problem cannot be solved analytically!**Phase Plots**• Thornton and Marion 3-15 • Underdamped Oscillator**Noninertial Reference Frames**• Thornton and Marion Example 10.2 • Hockey Puck on a Merry-Go-Round**Electromagnetism**• Griffith’s 3-25 • Cylinder (radius R) with charge density σ() = k sin(5) • Answer:**Quantum Mechanics**• Griffiths 2.17 (1st ed.) • Time evolution of particle in even mixture of ground- and first-excited states of harmonic oscillator potential.**Quantum Mechanics - Project**See Stuart Farrell’s Spring 2005 CS-AAPT talk.**Optics**Fringe patterns on a holographic plate.**Optics – Final Exam Question**Diffraction intensity for a rectangular aperture.**Computational Physics**• Giordano and Nakanishi “Cream in the Coffee” Problem • Animation is a must!**Cream in the Coffee**Show the entropy’s progression toward a constant value.**Fluid Mechanics Project**Velocity field of fluid moving around rectangular obstruction.**Fluid Mechanics Project**Stream function of fluid moving around rectangular obstruction.**Fluid Mechanics Project**Vorticity of fluid moving around rectangular obstruction.

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