2 How this connects to your other standards

Mechanics is not sealed off from your other standards. Read this first if you are also taking one of the standards below.

How this connects

The most direct links, roughly in order of how often they actually come up:

Differentiation methods (91578): SHM IS a differential equation a = −ω²x means acceleration is the second derivative of displacement, so SHM is really d²x/dt² = −ω²x. Differentiating x = A cos(ωt) twice with the chain rule gives exactly −ω²x, which is why cosine describes SHM at all. Electrical Systems (91526): an LC circuit oscillates like a mass on a spring An LC circuit's charge obeys the same differential equation as SHM, just with charge in place of displacement. The physics is identical; only the symbols change — and the phasor diagram used for AC circuits is the same rotating-vector picture used here for circular motion. Integration methods (91579): SHM energy comes from integrating force The SHM energy result E = ½kA² is derived by integrating the restoring force F = −kx over displacement — work done = ∫F dx. Integrating acceleration also recovers velocity and displacement, the reverse of the differentiation link above. ✓

The big picture in one sentence

Circular motion, rotation, SHM and orbital motion are the same handful of ideas — a restoring influence, a periodic repetition, a conserved quantity — appearing in different costumes, and calculus is the language that shows they are the same underneath.

Practice for this standard covers the whole topic — flashcards and quiz.