17.3 Damped and forced oscillations, resonance
- Syllabus
- 9702–2028–2029
- Topic
- 17.3
- Level
- A2
Learning objectives
17.3.1A resistive force acting on an oscillating system causes damping• understand that a resistive force acting on an oscillating system causes damping17.3.2The terms light, critical and heavy damping and sketch displacement–time• understand and use the terms light, critical and heavy damping and sketch displacement–time graphs illustrating these types of damping17.3.3Resonance involves a maximum amplitude of oscillations and that this occurs• understand that resonance involves a maximum amplitude of oscillations and that this occurs when an oscillating system is forced to oscillate at its natural frequency
Damping removes energy from an oscillator and reduces its amplitude
A resistive force opposing motion transfers energy from an oscillating system to other stores, causing the amplitude to decrease with time.
The damping force may depend on speed; distinguish the ideal SHM frequency from the changed response of a damped system.
Air resistance makes a pendulum’s swings gradually smaller because mechanical energy becomes thermal energy in the air.
Damping does not necessarily stop oscillation immediately, and reduced amplitude is not the same as reduced equilibrium position.
Light, critical and heavy damping describe how quickly oscillations return to equilibrium
Light damping allows oscillations with decreasing amplitude; critical damping returns to equilibrium fastest without oscillating; heavy damping returns more slowly without overshoot.
Sketch displacement against time with or without crossings of equilibrium and compare settling time, not just initial slope.
A door closer is designed near critical damping so the door settles promptly without repeated swinging.
Critical damping is not “maximum resistance” in every situation; too much damping can make return slower.
Resonance gives maximum amplitude when driving and natural frequencies are equal
| Term | Meaning |
|---|---|
| natural frequency | frequency at which the system oscillates freely after disturbance, with no periodic driving |
| driving frequency | frequency of the external periodic force |
| resonance | maximum steady oscillation amplitude when driving frequency equals natural frequency |
At resonance the driving force transfers energy to the oscillator most effectively on successive cycles. The amplitude grows until energy supplied per cycle balances energy dissipated by damping.
A graph of steady amplitude against driving frequency has one peak at the natural frequency in the syllabus model. Away from that frequency the amplitude is smaller.
| Increased damping | Change to resonance curve |
|---|---|
| more energy lost per cycle | lower maximum amplitude |
| response spread over a wider frequency range | broader, less sharp peak |
Regular pushes on a swing at its natural period add energy in step and build maximum amplitude; pushes at another frequency drift out of step and transfer less energy overall.
For the assessed definition, say driving frequency equals natural frequency—not merely that it is nearby. Resonance need not be destructive and does not require zero damping.