Oscillations in a driven spring

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Discussion Overview

The discussion revolves around the behavior of a spring when driven at a frequency different from its resonance frequency. Participants explore the nature of oscillations in a driven spring, particularly focusing on the relationship between the driving frequency and the resonance frequency, as well as the resulting amplitude variations.

Discussion Character

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

Main Points Raised

  • One participant suggests that a spring driven at a frequency fdrive will oscillate in a superposition of frequencies, specifically the driving frequency and the resonance frequency fres.
  • Another participant asserts that if the driving amplitude remains constant, the spring will oscillate at the driving frequency fdrive.
  • A question is raised about whether the amplitude of the spring's oscillation will vary when driven at a constant amplitude.
  • One participant expresses the belief that variations in amplitude may occur due to resonance effects, suggesting that if fdrive is close to fres, the spring's oscillation might exhibit interference patterns leading to amplitude modulation.
  • A later reply discusses the relationship between the natural frequency and the driving frequency, indicating that while the natural frequency influences the system, the steady-state solution will occur at the excitation frequency only, particularly when close to resonance.

Areas of Agreement / Disagreement

Participants express differing views on whether the amplitude of oscillation will vary when driven at a constant amplitude, indicating a lack of consensus on this aspect of the discussion.

Contextual Notes

Some assumptions regarding the nature of resonance and the effects of internal friction and windage are mentioned but not fully explored, leaving some mathematical and conceptual details unresolved.

entropy1
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If I have a spring with resonance frequency fres and I drive it with frequency fdrive, the spring will oscillate in a superposition of two frequencies, right?

Which frequencies are they?
 
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If you keep driving it with the same amplitude it will oscillate with fdrive.
 
mfb said:
If you keep driving it with the same amplitude it will oscillate with fdrive.
Will the spring's oscillation vary in amplitude (if de driver amplitude is constant)?
 
Why would you expect any variation?
 
mfb said:
Why would you expect any variation?
I think because of the resonance; the spring tends toward it. For instance: if fdrive=fres+d with d a small number, the spring's resonance frequency will interfere with the driver's frequency and produce a slow oscillation fres-fdrive I suspect. I recall having seen this at high school but I'm not sure. It is like the spring's phase aligning with the driver's phase and then run out of phase and run back in it again. Is this correct?

That would be a modulation I guess.
 
Last edited:
Motion at the natural frequency is associated with the homogeneous solution of the ODE. Even if it is not included in the mathematical formulation, in reality it will die away due to internal friction and also windage.

The steady solution is due solely to the excitation and will occur at the excitation frequency only. If the excitation is close to the natural frequency, the amplitude of the steady state solution will be quite large. This is what is known as resonance.
 

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