Oscillator driving frequencies

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Discussion Overview

The discussion revolves around the behavior of oscillators when subjected to periodic external frequencies, specifically addressing why the amplitude of oscillations does not start at zero in certain graphs. The scope includes theoretical considerations and technical explanations related to oscillatory motion and external driving forces.

Discussion Character

  • Technical explanation, Conceptual clarification

Main Points Raised

  • One participant questions why the periodic external frequency applied does not start at zero on the graphs of oscillators.
  • Another participant clarifies that the graph does start at zero for the input frequency, noting that when the input frequency is zero, the frequency ratio also becomes zero.
  • A participant corrects their earlier statement, indicating they meant to refer to the amplitude of the oscillations instead of the frequency.
  • It is proposed that if the force has constant amplitude, the amplitude of oscillations remains approximately constant at low frequencies due to the relationship between the mass, acceleration, and spring constant in the equation of motion.
  • Different scenarios for plotting oscillation behavior are presented, including cases where the force amplitude is constant, proportional to frequency, or proportional to frequency squared.
  • It is noted that many plots do approach zero amplitude when the frequency is zero, although this may depend on the specific conditions of the system.

Areas of Agreement / Disagreement

Participants express differing views on the behavior of amplitude at low frequencies, with some suggesting it remains non-zero under certain conditions while others indicate that it can approach zero depending on the plot type. The discussion does not reach a consensus on these points.

Contextual Notes

Limitations include the dependence on the definitions of force amplitude and the specific physical situations being considered, as well as the unresolved nature of how different plots may behave at zero frequency.

Saado
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I've attached a graph to this post. Why is it that the periodic external frequency applied never starts at 0 on graphs like these?
 

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It does start at 0 on the graph you posted.
##\omega_A## is the input frequency (or periodic external frequency). When ##\omega_A = 0##, the frequency ratio ##\omega_A\omega_0 = 0##.
 
Sorry my bad I meant the amplitude of the oscillations.
 
If the force has constant amplitude, at low frequencies the ##m\ddot x## term is small compared with the ##kx## term in the equation of motion, so the amplitude is approximately ##F/k##. That is why the amplitude doesn't go to 0 as the frequency goes to 0.

Note, these type of plots can be drawn in different ways, corresponding to different physical situations:

1. The force has constant amplitude, like your attachment
2. The force amplitude is proportional to the frequency
3. The force amplitude is proportional to the frequency squared (for example the unbalanced force on a rotating object)

You can also plot how the velocity, and acceleration of the system changes with frequency.

Most of those plots do go to 0 when the frequency is 0.
 
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