Simple Harmonic Motion – AP Physics 1

Learning Objectives

Describe oscillatory motion of a mass-spring system

Relate period to mass and spring constant: T = 2π√(m/k)

Analyze energy interchange between KE and PE

Understand how damping affects amplitude over time

Key Equations

\( x(t) = A\cos(\omega t + \phi) \)

\( \omega = \sqrt{k/m} \)

\( T = 2\pi\sqrt{m/k} \)

\( E = \tfrac{1}{2}kA^2 \)

\( KE = \tfrac{1}{2}mv^2,\; PE = \tfrac{1}{2}kx^2 \)

Why It Matters

SHM is everywhere — from clock pendulums to atoms vibrating in crystals. Understanding it unlocks wave physics, AC circuits, and quantum mechanics. The key insight: the restoring force is proportional to displacement.