AP Physics C: Mechanics ›  Unit 7

Unit 7 Oscillations

Springs, pendulums, and everything that goes back and forth. The final unit of the year — and the one where force, energy, and rotation all show up in the same problem at once.

📋 10–15% AP Exam Weighting🕐 ~12–17 Class Periods📺 5 Episodes✅ Progress Check 7
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Episode Guide — Season 7

EP.7.1

Defining Simple Harmonic Motion (SHM)

SHM shows up wherever a restoring force is proportional to displacement — F = −kx. That single condition is the seed everything else in this unit grows from.

F = −kxRestoring forceEquilibrium position
🕐 2–3 class daysOpen lesson →
EP.7.2

Frequency and Period of SHM

A spring's period depends on mass and stiffness; a pendulum's depends on length and gravity. Neither one cares about amplitude.

T = 2π√(m/k)T = 2π√(l/g)Period independent of amplitude
🕐 2–3 class daysOpen lesson →
EP.7.3

Representing and Analyzing SHM

Position, velocity, and acceleration all trade off as sines and cosines of the same phase. The differential equation behind it all is one you're now expected to recognize on sight.

x(t) = A cos(ωt + φ)d²x/dt² = −ω²xPhase relationships
🕐 3–4 class daysOpen lesson →
EP.7.4

Energy of Simple Harmonic Oscillators

Kinetic and potential energy trade places continuously, but the total never moves. Change the amplitude and you change how much energy the system is carrying, not how fast it oscillates.

E = K + UE_total = ½kA²K max ↔ U min
🕐 2–3 class daysOpen lesson →
EP.7.5

Simple and Physical Pendulums

Swap Newton's second law for its rotational form and small-angle pendulums fall right into the same SHM pattern — whether they're a point mass on a string or a swinging rigid body.

T = 2π√(I/mgd)Small-angle approximationSimple vs. physical pendulum
🕐 3–4 class daysOpen lesson →
🎓 AP Classroom — Progress Check 7
~18 multiple-choice · 4 free-response · Covers all 5 episodes
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