Key Concepts: Simple Harmonic Motion (SHM)

What is SHM?

• A type of periodic motion where the restoring force is proportional to displacement: F = −kx.
• The motion repeats in a sinusoidal pattern — described by sine or cosine functions.

Key Equations

• Position: x(t) = A cos(ωt + φ).
• Velocity: v(t) = −Aω sin(ωt + φ). Maximum speed = Aω (at equilibrium).
• Acceleration: a(t) = −Aω² cos(ωt + φ) = −ω²x. Maximum acceleration = Aω² (at extremes).

Examples of SHM

• Mass on a spring: ω = √(k/m), T = 2π√(m/k).
• Simple pendulum (small angles): ω = √(g/L), T = 2π√(L/g).

Important Properties

• Acceleration is always directed toward the equilibrium position.
• Maximum displacement from equilibrium = amplitude (A).