Oscillation, resonance and phase
Введено| English | Значение |
|---|---|
| damping/ˈdæmpɪŋ/ | затухание |
| resonance/ˈrezənəns/ | резонанс |
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.
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.
Energy changes during one oscillation
In ideal SHM, speed is greatest at equilibrium while kinetic and potential energy exchange.
For ideal SHM, where is speed greatest?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
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.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
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.
In the lab: 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?
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
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
- 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.
Your turn: 30 cycles take 45 s. Find period.
30 cycles take 45 s. Find period.
Сложность 2/5 · 140 монет + небольшой бонус за первое выполнение сегодня
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.
Not true: Every periodic motion satisfies the condition for simple harmonic motion. 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.
- Simple harmonic motion has acceleration proportional to displacement and directed toward equilibrium.
- Velocity is greatest near equilibrium for ideal SHM, while acceleration magnitude is greatest at extreme displacement.
- Watch for: not every repeated motion is SHM.
Write from a period of 1.25 s
- 40 cycles take 50 s.
- Find the period and the frequency. Periodic motion is not always simple harmonic motion.
Every periodic motion satisfies the condition for simple harmonic motion.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
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.
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
resonance means A large response to periodic forcing near a natural frequency.
40 cycles take 50 s. What are the period and the frequency, and what extra condition does simple harmonic motion need?
Period is total time divided by the number of cycles. Frequency is 1 divided by the period.
What is the period?
Сложность 1/5 · 100 монет + небольшой бонус за первое выполнение сегодня
50 divided by 40 is 1.25 s. The prompt uses 30 cycles in 45 s, which is 1.5 s. Other options — 0.80 Hz (the frequency); 1.5 s (the prompt period).