Damped and forced oscillations
| English | Chinese | Pinyin |
|---|---|---|
| damping | 阻尼 | zǔ ní |
| resonance | 共振 | gòng zhèn |
| oscillator | 振子 | zhèn zi |
| forced oscillation | 受迫振动 | shòu pò zhèn dòng |
| driving force | 驱动力 | qū dòng lì |
| driving frequency | 驱动频率 | qū dòng pín lǜ |
| natural frequency | 固有频率 | gù yǒu pín lǜ |
A bell fades, a swing grows
- Strike a bell and it rings, then slowly fades — that fading is damping 阻尼.
- Push a swing at just the right rhythm and it grows huge — that is resonance 共振.
- Both come from how an oscillator 振子 handles energy.
Damping
- A resistive force (friction, drag) removes energy, so the amplitude shrinks over time.
- The lost energy turns into heat.
Resonance
Drive the swing at different frequencies. Far from its natural frequency it barely moves; tune them to match and the amplitude explodes — resonance, the same effect that can shake a bridge apart.
Damping of an oscillation is caused by:
Friction or drag carries energy away as heat, so each swing is smaller than the last.
Three kinds of damping
- Light: amplitude dies away slowly, still oscillating.
- Critical: returns to rest fastest, with no overshoot (a meter needle).
- Heavy: returns slowly with no oscillation (a strong door closer).
Critical damping settles fastest with no overshoot; heavy damping crawls back more slowly
Match each type of damping to its behaviour.
Critical damping returns to equilibrium in the shortest time without overshooting; heavy damping is slower still.
Forced oscillations 受迫振动
- A driving force 驱动力 of frequency $f_{\text{d}}$ pushes the system.
- The system then oscillates at the driving frequency 驱动频率, not its own natural one.
In light damping the amplitude dies away slowly over many cycles
A forced oscillator vibrates at:
It follows the driver — it oscillates at the driving frequency $f_{\text{d}}$.
Resonance
- Resonance: when $f_{\text{d}}$ equals the natural frequency 固有频率 $f_0$, the amplitude is largest.
- Lighter damping → a sharper, higher peak. (A swing, a wine glass, a building in an earthquake.)
Resonance happens when the driving frequency equals the ____ frequency.
At $f_{\text{d}} = f_0$ the driver feeds energy in most effectively and the amplitude peaks.
Lighter damping gives a sharper, higher resonance peak.
Less energy is lost each cycle, so the amplitude builds higher and the peak is narrower.
Select all the examples of resonance.
Each of the first three matches a driving frequency to a natural frequency. A rolling ball is not a driven oscillation.
You've got it
- damping = a resistive force shrinking the amplitude (energy → heat)
- light (slow decay), critical (fastest, no overshoot), heavy (slow, no oscillation)
- resonance: driving frequency = natural frequency → biggest amplitude (sharper if lightly damped)