Full Mock 8 — Oscillations and SHM Focus
Full Mock 8 for AP Physics C: Mechanics focuses on oscillations and SHM. Practice differential equation setup, energy in SHM, phase analysis, and FRQ derivation problems.
Differential Equations, Energy in SHM, and Phase Analysis
Full Mock 8 places the primary emphasis of AP Physics C: Mechanics Mock 8 on Unit 7 — Oscillations and Simple Harmonic Motion — while maintaining complete coverage of all other units. Unit 7 is the final unit of AP Physics C: Mechanics and is tested on every AP exam administration, yet students often under-prepare it relative to dynamics and rotational mechanics.
Emphasis Areas in Mock 8
Setting Up and Solving the SHM Differential Equation
A core FRQ task in Mock 8 is deriving the equation of motion for a physical system and identifying it as SHM. Starting from Newton's second law — for a spring-mass system, m(d²x/dt²) = -kx — students must recognise the ODE form, write the general solution x(t) = A cos(ωt + φ), verify it satisfies the ODE by substituting the second derivative, and determine A, ω, and φ from given initial conditions. Every one of these steps is separately credited in the rubric.
Energy Analysis in SHM
Mock 8 includes questions requiring students to express the total mechanical energy in SHM as E = (1/2)kA², derive the velocity as a function of position using energy conservation (yielding v(x) = ω√(A² - x²)), and sketch or interpret graphs of kinetic energy, potential energy, and total energy as functions of both position and time. The phase relationship between KE and PE — they sum to a constant while individually oscillating — is a frequent MCQ topic.
Phase Relationships Between Displacement, Velocity, and Acceleration
Since v(t) = dx/dt = -Aω sin(ωt + φ) and a(t) = -Aω² cos(ωt + φ), the velocity is 90° out of phase with the displacement and the acceleration is 180° out of phase. Mock 8 MCQs test recognition of these phase relationships by presenting graphs or equations of one quantity and asking for the form of another.
Skills Developed in Mock 8
- Deriving and solving the SHM ODE for standard physical systems (spring-mass, simple pendulum, physical pendulum).
- Applying initial conditions to determine A and φ from given x(0) and v(0).
- Computing speed at arbitrary position using energy conservation in SHM.
- Identifying and interpreting phase relationships between x(t), v(t), and a(t).
- Recognising that period depends on restoring force constant and mass, not on amplitude (for ideal SHM).
Beyond the Spring-Mass System
Mock 8 includes SHM scenarios beyond the standard spring-mass: a physical pendulum whose period requires applying τ = Iα and small-angle linearisation, and a block in a non-uniform potential well whose SHM is established by expanding U(x) about equilibrium. These contexts demand the same ODE-recognition and solution skills but in less familiar settings.