List of courses for which I’ve had to solve (for class, assignments, or tests) simple, damped, and driven harmonic oscillators:
Physics 1: The student encounters this recurrent and relentless creature for the first time.
Physics 2: Now with electricity!
Physics lab 1: First chance you actually get to see it in real spacetime. Still have to solve the equations again.
Physics lab 2: Now with electricity (2)!
Waves and oscillations: Well, it won’t be a course about oscillations without one or twelve.
Analytical Mechanics: First with Lagrangian, then with Hamiltonian, then with Hamiltonians and matrices.
Ordinary differential equations: “We will assume that this is the first time you have ever seen a linear second order differential equation.”
Partial differential equations: Special case for Sturm Liouville, all over the place.
Quantum Mechanics 1: But be discrete about it.
Quantum Mechanics 2: Once with Schrödinger picture; once with Heisenberg picture; interaction picture pending next homework set.
And the year has just started; I’m sure at least two more courses will add themselves to that list before this degree is all said and done.
Not that I mind it or anything. On the contrary. The harmonic motion is a neverdying beast, rising from the dead and possessing each course in its own spectral way. Each time, we, the students, are touched and are offered a unique glimpse at true Nirvana.
I can only hope that one day I too will truly embrace The Harmonic and become One with the Oscillating Truth.
Until then, I guess my CV will be organized hierarchically:
Vaguely familiar with: theories of space and time, theories of matter and light, topology and groups.
Strong with: oscillating point masses; oscillating mass points; oscillating charges; oscillating oscillations; oscillating scintillation; oscillation of moods and modes of oscillations.
Well, I guess that when all you have is an exponent, everything in life seems linear.