Oscillations and Waves
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Daily Schedule Term 4
See also Daily Schedule Term 5
Week 1 — Lightning Introduction to Mathematica Notebooks — Velocity of a Particle
- Tuesday, Jan. 14 — Preparation for class: Study Sections 1-3 of An Elementary Introduction to the Wolfram Language, 3rd Edition, hereafter abbreviated EIWL3 — Expressions, operator precedence, symbolic manipulation, built-in functions, and user-defined functions in Mathematica — We will work through a little demonstration called Heads or Tails which demonstrates user-defined functions and nested functions
- Friday, Jan. 17 — Problem Set 1: Solve all Sections 1-4 of EIWL3 — PS1 Solution — We learned four more notebook features that greatly enhance readability: plain text cells, section cells, subsection cells, and comments in code — In class, we worked through a small but critical bit of physics, Position from Velocity — Theory — We manually filled out a Position from Velocity - Constant Acceleration worksheet that demonstrates the theory we have developed so far for the case of linearly increasing velocity (aka constant acceleration or uniform acceleration)
Week 2 — Acceleration of a Particle — Newton’s 2nd Law — Interesting Complications
- Tuesday, Jan. 21 — Problem Set 2: Solve all of the exercises from Sections 5-8 of EIWL3 — PS2 Solution — Look ahead to Section 9 of EIWL3 — In class: We completed the Position from Velocity - Constant Acceleration notebook
- Friday, Jan. 24 — Problem Set 3: Solve all the exercises from Sections 9, 10, and the first half of Section 11 (Exs. 11.1 to 11.15) — PS3 Solution — In-class: We will develop Velocity from Acceleration - Theory and combine this with the theory we already developed for obtaining position from velocity — In other words, we will transitively obtain velocity from acceleration and then position from velocity — We will start to see how interesting complications can arise — Finally, in class, we will complete the Velocity from Acceleration - Sinusoidal Force notebook
Week 3 — Second-Order Runge-Kutta — Mass on a Spring — Damped Oscillation
- Wednesday, Jan. 29 — Problem Set 4: Solve the rest of the exercises from Section 11 (Exs. 11.16 to 11.31), Section 12, and Section 13 — PS4 Solution — In-class: Develop Second-Order Runge-Kutta - Theory and then complete the Second-Order Runge-Kutta - Mass on a Spring notebook — Period (T), frequency (f=1/T), and angular frequency (ω=2π f)
- Friday, Jan. 31 — No new assignment in EIWL3 — In-class: Develop General Second-Order Runge-Kutta - Theory and then complete the General Second-Order Runge-Kutta - Damped Oscillation notebook
Week 4 — Forced Oscillation — Resonance — Damped Pendulum — Animated Graphics
- Tuesday, Feb. 4 — Problem Set 5: Do the Exercises from Sections 14 and 17 — PS5 Solution — Additionally, instead of turning in the exercises from Sections 15 and 16, explore Mathematica and choose any topic on which to give a presentation — In-class: We will flesh out a little more of the General Second-Order Runge-Kutta - Best Estimate of Average and then proceed to your
- Friday, Feb. 7 — Instead of a new Problem Set: Before class, have the General Second-Order Runge-Kutta - Forced Oscillation notebook working — In-class: We will use the notebook you finished before class to analyze resonance — Develop theory to transition from the damped oscillator to the damped pendulum — Damped Oscillator to Damped Pendulum - Theory which introduces Angle, Angular Velocity, Angular Acceleration, and the Approximate Theoretical Solution — In-class: Start completing Damped Pendulum - With Animated Graphics notebook
Week 5 — Forced Pendulum — Phase Space — Chaos — Exam 1
- Tuesday, Feb. 11 — Problem Set 6: Re-download Damped Pendulum - With Animated Graphics notebook that we started in the last class and finish it — PS6 Solution — Problem Set 7: Do the exercises from EIWL3 Sections 18 and 19 — PS7 Solution — In-class: Examine Forced Pendulum - Phase Space - Chaos notebook
- Friday, Feb. 14 — Exam 1 - Naval Battle — Exam 1 Solution
Week 6 — Systems with Two Masses — Systems with Many Masses
- Tuesday, Feb. 18 — Problem Set 8: Do the Exercises from EIWL3 Sections 20, 21, and 22 — In-class: Develop Coupled Harmonic Oscillators - Theory and then complete the Coupled Harmonic Oscillators notebook
EIWL3 Sections 25-34, and Sections 38-41 are when we get to the grammar and a significantly more advanced understanding of the Wolfram Language. You already learned about options in Section 20. Now pay particular attention to Sections 25 and 26, which I deliberately spread across two problem sets so that they would have more time to sink in. These two sections start exposing the heart of functional programming.
- Friday, Feb. 21 — Problem Set 9: Do the Exercises from EIWL3 Sections 23, 24, and 25 — In-class: Complete the Many Harmonic Oscillators notebook
Week 7 — Double Pendulum
- Tuesday, Feb. 25 — Problem Set 10: Do the Exercises from EIWL3 Sections 26, 27, and 28 — In-class: Present Double Pendulum - Theory and then complete the Double Pendulum notebook
See also Daily Schedule Term 5
