Simple_harmonic_motion

# Simple harmonic motion ## Microsim > *Microsim pending. The pipeline is currently authoring and saving a sketch in the [p5.js Web Editor](https://editor.p5js.org). Once saved, this section will hold the editor URL, a 100-word description of what the sketch demonstrates, and the full source code.* **Editor URL:** `<paste editor URL after save>` **Description (100 words):** _<filled in at finalize>_ ```js // sketch.js will be inlined here once finalized ``` ## Links (Wikipedia order)  `Acceleration` · `Alexis_Clairaut` · `Amplitude` · `Analytical_mechanics` · `Angular_acceleration` · `Angular_displacement` · [[Angular_frequency]] · `Angular_momentum` · `Angular_velocity` · `Appell's_equation_of_motion` · `Applied_mechanics` · `Augustin-Louis_Cauchy` · `Bernard_Koopman` · [[Calculus]] · `Carl_Gustav_Jacob_Jacobi` · `Celestial_mechanics` · `Centrifugal_force` · `Centripetal_force` · [[Christiaan_Huygens]] · `Circle_group` · `Circular_motion` · `Classical_field_theory` · `Classical_mechanics` · `Complex_harmonic_motion` · `Continuum_mechanics` · `Coriolis_force` · `Couple_(mechanics)` · `D'Alembert's_principle` · [[Damping]] · `Daniel_Bernoulli` · [[Differential_equation]] · `Displacement_(geometry)` · `Dissipation` · [[Dynamics_(mechanics)]] · `Edmond_Halley` · `Edward_Routh` · `Elasticity_(physics)` · [[Energy]] · `Equations_of_motion` · `Euler's_equations_(rigid_body_dynamics)` · `Euler's_laws_of_motion` · `Exertion` · `Fictitious_force` · `Fixed_point_(mathematics)` · [[Force]] · [[Fourier_analysis]] · `Frame_of_reference` · `Frequency` · `Friction` · `Galileo_Galilei` · `Gravity` · `Hamiltonian_mechanics` · `Hamilton–Jacobi_equation` · `Harmonic_oscillator` · `Hertz` · `History_of_classical_mechanics` · `Hooke's_law` · `HyperPhysics` · `Impulse_(physics)` · `Inertia` · `Inertial_frame_of_reference` · `International_System_of_Units` · [[Isaac_Newton]] · `Isochronous_timing` · `Jeremiah_Horrocks` · `Johann_Bernoulli` · [[Johannes_Kepler]] · [[John_von_Neumann]] · `Joseph-Louis_Lagrange` · `Joseph_Liouville` · [[Josiah_Willard_Gibbs]] · `Kinematics` · `Kinetic_energy` · `Kinetics_(physics)` · `Koopman–von_Neumann_classical_mechanics` · `Lagrangian_mechanics` · `Leonhard_Euler` · `Linear_motion` · `List_of_textbooks_on_classical_mechanics_and_quantum_mechanics` · `Lorentz_oscillator_model` · `Mass` · [[Mathematical_model]] · `Mechanical_energy` · `Mechanical_equilibrium` · `Mechanics` · `Metre` · `Molecular_vibration` · `Moment_(physics)` · `Moment_of_inertia` · `Momentum` · `Motion` · `Net_force` · `Newton's_law_of_universal_gravitation` · [[Newton's_laws_of_motion]] · `Newton_(unit)` · `Non-inertial_reference_frame` · `Orbit_(dynamics)` · [[Ordinary_differential_equation]] · `Origin_(mathematics)` · [[Oscillation]] · `Particle` · `Paul_Émile_Appell` · [[Pendulum]] · `Pendulum_(mechanics)` · `Periodic_function` · `Phase_(waves)` · [[Phase_space]] · [[Physics]] · `Pierre-Simon_Laplace` · `Pierre_Louis_Maupertuis` · `Potential_energy` · `Projection_(mathematics)` · `Proportionality_(mathematics)` · `Rayleigh–Lorentz_pendulum` · `Reactive_centrifugal_force` · `Relative_velocity` · `Resonance` · `Restoring_force` · `Rigid_body` · `Rigid_body_dynamics` · `Rotating_reference_frame` · `Rotation_around_a_fixed_axis` · `Rotational_frequency` · `Routhian_mechanics` · `Scotch_yoke` · `Siméon_Denis_Poisson` · [[Sine_wave]] · `Small-angle_approximation` · `Space` · `Speed` · `Spring_(device)` · `Statics` · `Statistical_mechanics` · `Straight-line_mechanism` · `String_vibration` · `Tangential_speed` · `Time` · `Timeline_of_classical_mechanics` · `Torque` · [[Velocity]] · `Vibration` · `Virtual_work` · `William_Rowan_Hamilton` · `Work_(physics)` ## Media (PD/CC)  !Gif Library/Simple harmonic motion/Simple Harmonic Motion Orbit.gif *Simple_Harmonic_Motion_Orbit.gif · Public domain*   **Semiotic universals** (the notations and alphabet letters this article speaks — each opens its canonical card): crystal bravais · kanji radicals · harmonic · oscillation · energy. Index: the glyph gallery · SEMIOTICS PORTAL.  > **Room:** [[Energy]] · **Status:** ⏳ awaiting microsim · ← back to MAIN ## Overview Simple harmonic motion (SHM) is the recurring rhythm at the heart of nearly every oscillating [[System|system]] in classical [[Physics|physics]]: the unhurried swing of a [[Pendulum|pendulum]] at small amplitude, the bobbing of a mass on a spring, the back-and-forth of a tuning fork, the vibration of an atom in a crystal lattice. A system executes simple harmonic motion whenever its restoring [[Force|force]] is linearly proportional to displacement from equilibrium and directed back toward it — the textbook embodiment being Hooke's law, F = -kx, leading to the equation of motion m·x'' + k·x = 0 whose solutions are pure sinusoids of [[Angular_frequency|angular frequency]] omega = sqrt(k/m). The defining features are isochronism (period independent of amplitude), perfect energy exchange between kinetic and potential reservoirs, and a closed elliptical trajectory in [[Phase_space|phase space]]. SHM matters because almost any smooth potential, expanded around a stable minimum, looks quadratic to lowest order — so SHM becomes the universal first approximation for small oscillations everywhere, from molecular bonds to bridge cables. Adding linear [[Damping|damping]] yields exponential decay; adding a periodic drive yields resonance. SHM is therefore the gateway concept that organizes vibration, waves, AC circuits, optics, and the quantum harmonic oscillator under one mathematical roof. ## See also - Room hub: [[Energy]] - p5.js Editor conventions: P5 JS EDITOR - Wiki root: MAIN --- *Scaffolded by `generative-microsim` from row 0 of the Energy sheet on 2026-04-30T06:23:10Z.*  *Built to the [[WT!P5_js_Microsim_Master_Class|p5.js Master Class]].*   **Microsim — three.js (Wikitube framework):** *Simple harmonic motion* <div class="wt-sim" data-src="https://wikitube-3d-microsims.netlify.app/acoustics/Simple_harmonic_motion.html" data-title="Simple harmonic motion"></div> *Built from `MICROSIM_GUIDE/specs/acoustics/variants/Simple_harmonic_motion.json`; part of the [[PORTAL_Acoustics|Acoustics portal]] spine (section sims and See-also variants).*  ## Wikipedia : Wikitube **Strict pair:** [Wikipedia](https://en.wikipedia.org/wiki/Simple_harmonic_motion) : [Wikitube](https://en.wikitube.io/wiki/Simple_harmonic_motion) ## Previous hub tags Tree parent: [[Phase_space]]. Legacy hubs: `GENERATIVE`. --- *Sources: 1 legacy note. Minted wave 1, 2026-07-30 (v1.6 order).*