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Forced oscillations
Intermediate
System driven by an external periodic force.
A system driven at frequency ω_d settles to oscillate at ω_d (after transients) with amplitude depending on the closeness to its natural frequency. Maximum at resonance.
A child being pushed on a swing.
Steady-state frequency follows the driver, not the natural one.
In more detail
A forced oscillator is driven by an external periodic force. After transients die out, it oscillates at the driving frequency, with an amplitude that depends on how close that frequency is to the natural frequency.
Real-world uses
- Loudspeakers are forced oscillators driven by an electrical signal.
- Engine mounts are designed to isolate vibrations from driving frequencies.
- A child kept swinging by regular pushes is an example of a forced oscillation, where the driving force sets the frequency.
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Frequently asked questions
Does the system oscillate at its natural frequency?
Only during the transient. In steady state it follows the driving frequency.
What if the driving frequency is very high?
The amplitude becomes small, since the system cannot follow the rapid drive.
After a long time, what frequency does a forced system oscillate at?
At the driving frequency, regardless of its natural frequency, once the transient motion has died away.
Related topics in Oscillations & SHM
Damped oscillations · Underdamped, critical, overdamped · Quality factor · Resonance · Resonance examples · Amplitude vs frequency curve