Simple harmonic motion
In simple harmonic motion the restoring force is proportional to the displacement from equilibrium and always points back towards it, producing a smooth, repeating oscillation.
Practise this conceptSimple harmonic motion happens whenever the force pulling a system back toward equilibrium grows in direct proportion to how far it has been pushed away — twice the displacement means twice the restoring force, always aimed back the way it came.
A mass on a spring and a swinging pendulum (for small swings) both follow this pattern, and both produce the same smooth, repeating back-and-forth motion as a result, even though the physical setups look nothing alike. That's the payoff of "simple harmonic": the same mathematics describes wildly different systems.
One property surprises people: for an ideal simple harmonic oscillator, the period doesn't depend on the amplitude at all. A pendulum swinging through a small arc and the same pendulum swinging through a larger one (still within the small-angle approximation) take the same time per swing — the larger swing covers more distance, but it also moves faster to cover it in the same time.
Key ideas
Requires: Newton's second law
Unlocks: Coupled and driven oscillators, Damped oscillations, LC and RLC oscillations, Resonance, Standing waves, The quantum harmonic oscillator, The wave equation
Formulas
| Symbol | Name | Unit |
|---|---|---|
| period | s (second) | |
| distance | m (metre) |
Common misconceptions
- The restoring force in simple harmonic motion is constant, not proportional to displacement.
- An object in simple harmonic motion moves at constant speed throughout its oscillation.
- The period of a simple harmonic oscillator depends on its amplitude.
Resources
Part of these UT courses
This concept is mapped as covering part of the following course(s) in the University of Tartu curriculum.
- The physical world viewLOFY.01.002
- OpticsLOFY.01.008
- Mechanics and heatLTFY.01.006