Oscillation

The AP CEDs name a whole unit Oscillations without ever defining the bare word. What they define is the special case inside it, and the gap between the two is where the marks live.

What makes anything oscillate. Two conditions, both from Topic 7.1. EK 7.1.A.2.ii: an equilibrium position is a location at which the net force exerted on an object or system is zero. EK 7.1.A.2.i: a restoring force is a force exerted in a direction opposite to the object's displacement from an equilibrium position. Displace the system, get pushed back, overshoot, repeat.

What makes it simple harmonic. EK 7.1.A.2 adds one more requirement: SHM results when the magnitude of the restoring force is proportional to the object's displacement from equilibrium, which is $F = -k\Delta x$. Pushing back is enough to oscillate. Pushing back in proportion is what fixes the period and licenses $T_s = 2\pi\sqrt{m/k}$ and $T_p = 2\pi\sqrt{\ell/g}$.

A case that oscillates without being SHM. A pendulum at large amplitude. AP Physics C: Mechanics EK 7.5.A.2.i gives its restoring torque as $\tau = -mgd\sin\theta$, and $\sin\theta$ is not proportional to $\theta$ once $\theta$ grows. The swing still repeats. The period formula stops being right.

One oscillation is one full cycle, back to the same position moving the same way, and the time it takes is the period. Counting half a swing as a cycle halves every answer downstream.

AP Physics C: Mechanics also attaches resonance to the idea, at 7.3.A.4: resonance occurs when an external force is exerted at the natural frequency of an oscillating system, and it increases the amplitude of the motion.

Worked spring and pendulum problems belong to the simple harmonic motion guide.