Physics HL · Chapter 12: Simple Harmonic Motion
Chapter 12 Wrap-Up
Consolidate SHM into one robust solve routine connecting model test, equations, phase interpretation, and energy methods.
Estimated time: 9 minutes
A Reliable SHM Workflow
Start by testing model validity: does acceleration point toward equilibrium and scale linearly with displacement in the regime considered? If yes, activate SHM tools. Then choose the representation that matches given data: graph slope for omega, sinusoidal equations for time-state questions, or energy forms when displacement and speed are mixed.
Keep phase language precise. Initial phase angle encodes your time-origin choice; phase difference compares two oscillators. Keep energy boundaries active as numerical checks: kinetic must vanish at turning points, and total energy must stay constant in ideal conditions.
Key Takeaways
- SHM requires a linear restoring relation a = -omega^2 x.
- Period and frequency satisfy f = 1/T, with omega = 2pi/T.
- Spring and small-angle pendulum periods follow T = 2pi sqrt(m/k) and T = 2pi sqrt(L/g).
- Displacement, velocity, and acceleration are sinusoidal and phase-linked.
- Phase difference is angular and maps to timing through Delta phi = 2pi(Delta t/T).
- In ideal SHM, energy transfers between E_p and E_k while E_T remains constant.
- Useful compact forms include E_k = (1/2)momega^2(A^2-x^2) and v = ±omega sqrt(A^2-x^2).
- Maximum-value data (vmax, amax) can recover omega, period, and amplitude quickly.
No new simulation is introduced in this wrap-up section because synthesis is the objective. Reuse the chapter simulation modes as a diagnostic loop: change one variable, predict graph and energy consequences in words, then verify numerically before moving on.