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Driving frequency, f_d
● VERBATIM — examined word-for-wordThe frequency of the external periodic force applied to the system. It belongs to the driver, not the system — a forced oscillation settles at the driving frequency, not at f₀. Amplitude of the response depends on how close f_d is to f₀.
What this actually means
f_d belongs to the driver, full stop. Once the initial transients die away, a forced system oscillates at f_d, not at its own natural frequency.
What f₀ controls is the SIZE of that response: large amplitude when f_d sits near f₀, small when far away.
Exam phrasing to expect: 'at what frequency does the system oscillate?' Answer: the driving frequency.
Prove it — watch it be true
- Set f_d well away from f₀ and let the motion settle
- The system oscillates at f_d, just with a small amplitude
- Sweep f_d towards f₀: frequency follows the driver, amplitude follows the match