Oscillation, resonance and phase
| English | 中文 | Pinyin |
|---|---|---|
| damping/ˈdæmpɪŋ/ | 阻尼 | zǔ ní |
| resonance/ˈrezənəns/ | 共振 | gòng zhèn |
What would explain this observation?
- A swing gains a large amplitude when pushes arrive with the right timing. The forcing frequency and damping 阻尼 help determine the response.
- Start with a prediction. State the quantities or features you would compare, then decide what evidence could distinguish two explanations.
Build the model
- Simple harmonic motion has acceleration proportional to displacement and directed toward equilibrium. Period is time per cycle; frequency is its reciprocal. Damping transfers energy away from the oscillating system.
- resonance 共振: A large response to periodic forcing near a natural frequency; damping: Energy transfer out of an oscillating system.
For ideal SHM, where is speed greatest?
Velocity is greatest near equilibrium for ideal SHM, while acceleration magnitude is greatest at extreme displacement. Resonance can occur near the natural frequency under periodic driving, with amplitude limited by damping.
Match each technical term to its precise meaning.
Use the definitions to distinguish related quantities and processes.
Choose evidence that can test it
- Velocity is greatest near equilibrium for ideal SHM, while acceleration magnitude is greatest at extreme displacement. Resonance can occur near the natural frequency under periodic driving, with amplitude limited by damping.
- Measure time for several complete oscillations and divide. Define a cycle consistently and use a small displacement when the model requires it. Keep pendulum paths clear and record damping effects rather than assuming perfect motion.
Which two habits make the investigation or model in this case more defensible?
Measure time for several complete oscillations and divide. Define a cycle consistently and use a small displacement when the model requires it. Keep pendulum paths clear and record damping effects rather than assuming perfect motion.
Work from known quantities
- State the known values and their units. Choose the relation because its assumptions fit this case, then rearrange before substitution.
- Known: 20 cycles take 32 s. T=total time/cycles=32/20=1.6 s. Frequency=1/T=1/1.6=0.625 Hz. A shorter total timing interval would make reaction-time error a larger fraction of the measurement.
30 cycles take 45 s. Find period. Use the same sequence: known quantities → model → relation → substitution → unit and interpretation.
30 cycles take 45 s. Find period.
The result is 1.5 s. Known: 20 cycles take 32 s. T=total time/cycles=32/20=1.6 s. Frequency=1/T=1/1.6=0.625 Hz. A shorter total timing interval would make reaction-time error a larger fraction of the measurement.
Check the conclusion and its limits
- Not every repeated motion is SHM. A force proportional to displacement but directed away from equilibrium does not produce SHM.
- Return to the original observation. Explain what the result supports, which conditions it assumes, and one way to test a competing explanation.
Every periodic motion satisfies the condition for simple harmonic motion. This claim is false: Not every repeated motion is SHM. A force proportional to displacement but directed away from equilibrium does not produce SHM.
Oscillation, resonance and phase: Velocity is greatest near equilibrium for ideal SHM, while acceleration magnitude is greatest at extreme displacement. Resonance can occur near the natural frequency under periodic driving, with amplitude limited by damping.
Every periodic motion satisfies the condition for simple harmonic motion.
Not every repeated motion is SHM. A force proportional to displacement but directed away from equilibrium does not produce SHM.
A large response to periodic forcing near a natural frequency: write the technical term.
resonance means A large response to periodic forcing near a natural frequency.