The frequency of forced oscillations

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Discussion Overview

The discussion revolves around the frequency of forced oscillations, particularly focusing on the relationship between the frequency of an oscillator and the frequency of an applied sinusoidal force. Participants explore concepts related to resonance, phase relationships, and the effects of non-sinusoidal forces on oscillators.

Discussion Character

  • Exploratory
  • Technical explanation
  • Conceptual clarification
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • Some participants assert that the frequency of an oscillator matches the frequency of a sinusoidal force, questioning how to visualize this relationship.
  • Others propose that an ideal oscillator resonates only at the fundamental frequency of the impressed force, acting as a filter that distorts the original waveform in amplitude and phase without changing frequencies.
  • A participant suggests a practical visualization involving pushing a swing to illustrate energy addition in phase with the oscillator.
  • Another participant seeks clarification on whether the applied sinusoidal force is in phase with the natural restoring force at resonance frequency.
  • One participant hypothesizes that if pushes are applied at the highest point of the swing, the displacement would increase until the swing's frequency matches the frequency of the pushes, potentially raising the swing's lowest position.

Areas of Agreement / Disagreement

Participants express various viewpoints on the relationship between the oscillator's frequency and the applied force, with some agreeing on the filtering nature of oscillators while others question specific phase relationships and effects of non-sinusoidal forces. The discussion remains unresolved with multiple competing views.

Contextual Notes

The discussion includes assumptions about ideal oscillators and does not resolve the implications of non-sinusoidal forces or the specific conditions under which phase relationships hold.

TheLil'Turkey
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So the frequency of an oscillator is always the same as the frequency of the force, if that force is a sinusoidal function of time. What's the best way to visualize why this is so? And also, why is the frequency of the oscillator in phase with the force if the force is below the resonance frequency of the oscillator, but 180 degrees out of phase with it if the frequency of the force is above the resonance frequency?

If the force has a constant frequency, but is not sinusoidal, does the oscillator also end up with that same frequency?
 
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The (ideal) oscillator will only resonate at the fundamental of the impressed force. It is a filter so the resultant oscillation will be a band-passed version with lots of phase shift so the original waveform will be distorted in amplitude and phase. But no frequencies can change.
 
One excellent way to visualize the addition of forces to an oscillator: put your girlfriend on a playground swing. Push her once, wait for her to swing forward, then backward. When she just stops her backswing, apply a small push. You have just added energy in phase with the SHM oscillator. Now, imagine pushing her in the same direction, but when she is at the highest point of her forward swing. What happens then?
 
sophiecentaur said:
The (ideal) oscillator will only resonate at the fundamental of the impressed force. It is a filter so the resultant oscillation will be a band-passed version with lots of phase shift so the original waveform will be distorted in amplitude and phase. But no frequencies can change.
I didn't understand all that, but I'd like to know if the applied sinusoidal force is in phase with the natural restoring force of the oscillator if the frequency of the applied force is the resonance frequency.

Bobbywhy said:
One excellent way to visualize the addition of forces to an oscillator: put your girlfriend on a playground swing. Push her once, wait for her to swing forward, then backward. When she just stops her backswing, apply a small push. You have just added energy in phase with the SHM oscillator. Now, imagine pushing her in the same direction, but when she is at the highest point of her forward swing. What happens then?
I think that what would happen is her displacement would slowly increase with every push until the angle becomes so great that her frequency becomes equal to the frequency of my pushes. Her lowest position during these oscillations would be higher than the lowest possible position of the swing. Is that right?
 

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