Unit 7 · 7.1 — Defining Simple Harmonic Motion (SHM)

Everything to learn here

• Concept: Simple Harmonic Motion occurs exclusively when a system is subjected to a restoring force and acceleration that are both directly and linearly proportional to the negative of the displacement from equilibrium.
• Equation: $$F_{net}=-kx\text{(The linear restoring force constraint defining SHM)}$$
• Equation: $$a=-(\frac{k}{m})x\text{(Acceleration explicitly as a function of position)}$$
• Equation: $$a=-({\omega }^2)x\text{(Acceleration as a function of angular frequency and position)}$$
• Vocabulary: Simple Harmonic Motion (SHM) — Periodic, repeating motion governed purely by a linear restoring force
• Vocabulary: Restoring Force — A force that continuously pushes or pulls a displaced system back toward its central equilibrium position
• Skill: Argumentation — Proving analytically whether a newly proposed force model (e.g., F = -kx^2) qualifies as SHM or merely periodic motion by checking for linearity

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