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Volume I · MMXXVI AP Physics C: Mechanics
Library› AP Physics C: Mechanics› Unit 7: Oscillations
⁂   AP Physics C: Mechanics · Unit 7

7. Oscillations

10–15% of the AP exam. 8 key topics. 4 common errors analyzed.

10–15% exam weight

Unit 7: Oscillations

Unit 7 (Oscillations) is part of the calculus-based AP Physics C: Mechanics curriculum. Variable-force problems and differential equations require calculus setup; show your integral expression before evaluating.

Key topics in this unit

  1. Defining Simple Harmonic Motion (SHM): restoring force proportional to displacement
  2. The SHM differential equation: d²x/dt² = −ω²x
  3. General solution: x(t) = A cos(ωt + φ)
  4. Period and frequency for a mass-spring system: T = 2π√(m/k)
  5. Period and frequency for a simple pendulum: T = 2π√(L/g) (small-angle approximation)
  6. Velocity and acceleration as functions of time in SHM
  7. Energy of SHM: total mechanical energy E = ½kA² = ½mv²_max; KE-PE exchange
  8. Physical pendulums: T = 2π√(I/mgd); requires moment of inertia

Common errors — what the rubric penalizes

These are the most frequently penalized mistakes on AP exam FRQs and MCQs. Review each before your next practice session.

Common error

Failing to recognize a(t) = −ω²x(t) as the diagnostic signature of SHM, and therefore not identifying SHM in problems where the equation of motion is given in differential-equation form rather than stated explicitly

Common error

Confusing the simple pendulum period formula (T = 2π√(L/g), valid for a point mass on a massless string) with the physical pendulum formula (T = 2π√(I/mgd)), and applying the simpler formula to distributed-mass pendulums where moment of inertia is required

Common error

Energy bookkeeping errors: setting ½kA² equal to only kinetic or only potential energy at an intermediate position, rather than recognizing E_total = KE + PE = ½kA² is constant while individual terms vary

Common error

Using ω = 2πf and T = 1/f interchangeably without tracking units, leading to factor-of-2π errors when computing maximum speed (v_max = ωA) or maximum acceleration (a_max = ω²A)

Study checklist

  • Can you list all key topics from memory without this page?
  • Have you worked through at least one FRQ-style question per topic?
  • Can you explain each common error above — and why the correct answer differs?
  • Have you reviewed the relevant College Board CED section and formula sheet entries?
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