| English | 意味 |
|---|---|
| damping/ˈdæmpɪŋ/ | 減衰 |
| resonance/ˈrezənəns/ | 共振 |
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?
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
In SHM, kinetic energy is greatest where the restoring force has done the most work - at equilibrium, where displacement and acceleration are zero. At maximum displacement the oscillator is instantaneously at rest.
Match each technical term to its precise meaning.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
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?
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
Stating the conditions and assumptions lets others repeat the work exactly, and recording the supporting evidence lets them check the conclusion. Hiding disagreeing results removes the evidence that could challenge a wrong conclusion, and one measurement can never establish a wider claim.
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.
難易度 2/5 · 140 コイン + 今日初回完了時に小ボーナス付与
The result is 1.5 s. Known: 30 cycles in 45 s. Use period = total time / cycles. T = 45/30 = 1.5 s. Timing many cycles and dividing reduces the effect of reaction-time error.
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: SHM needs a restoring force proportional to displacement and directed TOWARD equilibrium. Motion that merely repeats - a bouncing ball, a circular orbit - is periodic without satisfying that condition.
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.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
SHM needs a restoring force proportional to displacement and directed TOWARD equilibrium. Motion that merely repeats - a bouncing ball, a circular orbit - is periodic without satisfying that condition.
A large response to periodic forcing near a natural frequency: write the technical term.
難易度 1/5 · 100 コイン + 今日初回完了時に小ボーナス付与
resonance means A large response to periodic forcing near a natural frequency.