← all cardsTopic 8 · Oscillations · Forced oscillations & resonance
Free vs forced
Free: oscillates at its natural frequency f₀ after a single displacement. Forced: driven by an external periodic force, oscillates at the driving frequency with amplitude depending on how close f_d is to f₀.
What this actually means
Free oscillation: displace once, let go, and the system rings at its own natural frequency f₀.
Forced oscillation: an external periodic force feeds it continuously, and the settled motion runs at the driving frequency, not at f₀.
The response amplitude is the bridge between the two ideas: it depends on how close f_d sits to f₀.
Prove it — watch it be true
- Run free damping: the system picks its own frequency
- Now drive it at a chosen f_d: the settled motion follows the driver
- Move f_d closer to f₀: frequency still the driver's, amplitude growing