Compute the period of a pendulum and a mass-spring system, and describe the basic anatomy of a wave and the difference between transverse and longitudinal waves.
Simple harmonic motion (SHM) is back-and-forth motion around an equilibrium position, driven by a restoring force proportional to displacement -- Hooke's law's F=k*x is the classic example. Two familiar SHM systems have clean period formulas: a simple pendulum, T = 2*pi*sqrt(L/g), which depends ONLY on its length and gravity -- notably NOT on the mass of the bob or (for small swings) on how far it is pulled back to start, which is exactly why old pendulum clocks are tuned by adjusting the pendulum's length. A mass on a spring has T = 2*pi*sqrt(m/k), depending on mass and the spring's stiffness, again independent of amplitude.
A wave is a traveling disturbance that transports ENERGY without transporting matter itself -- picture a stadium wave, where the wave clearly moves around the stadium while each individual fan only ever moves up and down in place. Every wave has an amplitude (maximum displacement from equilibrium), a wavelength (the distance between two identical points, like crest to crest), a period (time for one full cycle), and a frequency (cycles per second, f=1/T, in hertz). Waves split into two families based on how the disturbance relates to the direction of travel: transverse waves disturb perpendicular to the direction of travel (a wiggled rope, light), while longitudinal waves disturb along the same direction as travel, as compressions and stretches (sound, coming next week).
Mastery looks like: They compute the period of a pendulum or a mass-spring system from its defining formula, and correctly distinguish transverse from longitudinal waves with a real example of each.
Common stumbles: Believing a heavier pendulum bob swings slower (or faster); confusing wavelength (a distance) with period (a time).