← Physics C: Mechanics syllabus

United StatesPhysics C: Mechanics

Unit 7: Oscillations

5 dot points across 5 inquiry questions. Click any dot point for a focused answer with worked past exam questions where available.

What defines simple harmonic motion, and why does a linear restoring force lead to the differential equation whose solution is sinusoidal?

Topic 7.1 Defining Simple Harmonic Motion: identify simple harmonic motion as arising from a linear restoring force, derive the defining differential equation, and recognize its sinusoidal solution.
A focused answer to AP Physics C: Mechanics Topic 7.1, covering the linear restoring force that defines simple harmonic motion, the differential equation $d^2x/dt^2 = -\omega^2 x$ , its sinusoidal solution, the meaning of the angular frequency, and the mass-spring example, with calculus-based worked examples.
10 min answer →

How does energy move between kinetic and potential forms in an oscillator, and how does conservation of energy fix the speed at any displacement?

Topic 7.4 Energy of Simple Harmonic Oscillators: express the kinetic, potential and total energy of an oscillator, apply conservation of energy to relate speed and displacement, and find the speed at any position.
A focused answer to AP Physics C: Mechanics Topic 7.4, covering the kinetic and elastic potential energy of an oscillator, the constant total energy $\tfrac{1}{2}kA^2$ , the exchange between forms through the cycle, finding the speed at any displacement by energy conservation, and the position where kinetic equals potential energy, with worked examples.
10 min answer →

How are frequency, period and angular frequency related, and how do they depend on the physical properties of the mass-spring and pendulum oscillators?

Topic 7.2 Frequency and Period of SHM: relate period, frequency and angular frequency, and determine them for the mass-spring system and the simple pendulum from the system properties.
A focused answer to AP Physics C: Mechanics Topic 7.2, covering the relationships between period, frequency and angular frequency, the period of a mass-spring oscillator and a small-angle simple pendulum, the amplitude-independence of the period, and how the period scales with mass, spring constant, length and gravity, with worked examples.
10 min answer →

How do the sinusoidal expressions for position, velocity and acceleration describe an oscillator, and how do we extract amplitude, phase and the maxima from them?

Topic 7.3 Representing and Analyzing SHM: write the sinusoidal position, velocity and acceleration of an oscillator, relate their amplitudes and phases, and read the motion from graphs and initial conditions.
A focused answer to AP Physics C: Mechanics Topic 7.3, covering the sinusoidal expressions for position, velocity and acceleration of an oscillator, the relationships among their amplitudes (vmax and amax), the phase relationships, reading amplitude and phase from initial conditions, and interpreting SHM graphs, with calculus-based worked examples.
11 min answer →

How do the simple and physical pendulums undergo simple harmonic motion at small angles, and how do we derive their periods using rotational dynamics?

Topic 7.5 Simple and Physical Pendulums: derive the small-angle period of the simple pendulum and the physical pendulum using the rotational form of Newton's second law and the small-angle approximation.
A focused answer to AP Physics C: Mechanics Topic 7.5, covering the simple pendulum and physical (extended-body) pendulum, deriving their small-angle periods from the rotational form of Newton's second law and the small-angle approximation, the role of rotational inertia and the distance to the center of mass, and when the SHM approximation breaks down, with calculus-based worked examples.
11 min answer →