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). This subtopic defines simple harmonic motion as motion in which acceleration is proportional to, and opposite in direction to, displacement, that is \(\ddot{x} = -n^2(x-c)\), producing a restoring force towards the centre of motion.

Students and teachers will cover how to verify that \(x = A\sin(nt+\alpha) + c\) is a solution, derive \(v^2 = n^2[A^2 - (x-c)^2]\), describe the motion using amplitude and period, prove that a given motion is simple harmonic, and model practical SHM problems in the HSC Extension 2 course.