Simple Harmonic Motion
This page covers the core ideas now; worked examples and practice problems will keep expanding.
1. Restoring Force
Simple harmonic motion happens whenever the restoring force on an object is directly proportional to its displacement from equilibrium, and points back toward that equilibrium. That single condition — not the specific system — is what defines SHM, which is why springs, pendulums, and even some electrical circuits all share the same mathematics.
The negative sign is the entire concept: force always opposes displacement, which is exactly what keeps pulling the system back toward equilibrium instead of letting it fly off.
2. Springs & Pendulums
kspring constant (N/m) — stiffness of the spring.mmass attached to the spring (kg).Lpendulum length (m).ggravitational acceleration (m/s²).
"A heavier pendulum bob swings slower." False — pendulum period depends only on length and g, not on mass. Doubling the bob's mass changes nothing about the period; this is exactly analogous to free fall, where mass also cancels out.
3. Energy in SHM
Total mechanical energy in SHM stays constant, continuously trading between kinetic and potential — maximum KE (and zero PE) at equilibrium, maximum PE (and zero KE) at the extremes of motion.
where A is the amplitude — the maximum displacement from equilibrium.
4. Simulator
5. Practice Problems
1. A 0.5 kg mass on a spring with k = 200 N/m oscillates. Find the period.