Oscillations and Waves

Daily Schedule Term 4

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 — PS01 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 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)

Tuesday, Jan. 21 — Problem Set 2: Solve all of the exercises from Sections 5-8 of EIWL3 — PS02 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) — 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

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 — In-class: Develop Second-Order Runge-Kutta - Theory and then complete the Second-Order Runge-Kutta - Mass on a Spring notebook
Friday, Jan. 31 — No new assignment in EIWL3 — In-class: There are three directions we can now go, having done the mass on a spring: (1) Two masses on two springs, but also coupled to each other, (2) Stick with one mass, but add in some realistic resistance (aka friction), so that the oscillation slowly dies down (most real systems have some resistance), (3) Add in an external driving force, so that as the oscillation dies down, the external driving force keeps it going — I will choose between these three directions before tomorrow’s class — I have decided I simply do not have time to create a new homework for Friday because of the Wed/Thu/Fri back-to-back classes this week, and I assume you will appreciate a breather for the same reason