Equations · equation
Simple Harmonic Motion
Mechanics · 1678
- Equation
- d²x/dt² = −ω²x ⇒ x = A cos(ωt + φ), ω = √(k/m)
- Field
- Mechanics
- Symbols
- x displacement from equilibrium · ω angular frequency · A amplitude · φ phase · k the restoring stiffness (Hooke's law) · m mass
- Year
- 1678
Significance
Whenever the restoring force is proportional to the displacement, the motion is a sinusoid with a period that does not depend on how big the swing is. A mass on a spring, a pendulum at small angles, a plucked string, an atom in a crystal lattice, an LC circuit — the same equation, and near any stable equilibrium every system looks like this to first order. That universality is why the sine wave is everywhere.
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