Simple Harmonic Motion

Simple harmonic motion is a major part of the Mechanics topic in NSW Year 12 Mathematics Extension 2 (NESA outcome ME2-12-05). In SHM the acceleration always points back towards a centre and grows in proportion to the distance from it, \(\ddot{x} = -n^2(x-c)\), so the restoring force makes the body oscillate about \(x = c\).

Students and teachers will cover checking \(x = A\sin(nt+\alpha) + c\) satisfies this equation, deriving \(v^2 = n^2[A^2 - (x-c)^2]\), finding amplitude, period and maximum speed, reading equations from graphs, proving a given motion is SHM, and modelling practical problems in the HSC Extension 2 course.