Forced oscillations vs Natural frequency

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Discussion Overview

The discussion revolves around the behavior of a spring mass system under forced oscillations, particularly focusing on the effects of phase differences between the forced oscillation frequency and the system's natural frequency. Participants explore concepts related to amplitude, phase relationships, and the implications of these factors on oscillatory motion.

Discussion Character

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

Main Points Raised

  • One participant suggests that a phase difference of Pi / 2 radians between the forced oscillation frequency and the natural frequency results in maximum amplitude for the spring mass system.
  • Another participant questions the notion of frequencies being "out of phase," arguing that frequency itself is a quantity and does not possess phase unless considering complex frequencies that account for dissipation.
  • A later reply proposes that the original poster may have intended to express the excitation force as F=cos(w*t - Pi/2).
  • Another participant seeks clarification on the relationship between phase difference and amplitude, suggesting that at the natural frequency, the phase difference should indeed be Pi / 2 radians, and expresses a belief that in-phase conditions lead to maximum amplitude.

Areas of Agreement / Disagreement

The discussion contains multiple competing views regarding the relationship between phase difference and amplitude in forced oscillations. There is no consensus on the correct interpretation of phase and frequency in this context.

Contextual Notes

Participants express uncertainty regarding the definitions of phase and frequency, and the implications of these concepts on the behavior of oscillatory systems. The discussion does not resolve these uncertainties.

Who May Find This Useful

This discussion may be of interest to those studying oscillatory systems, particularly in physics and engineering, as well as individuals exploring the concepts of forced oscillations and resonance.

Victorian91
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What happens if the frequency of the forced oscillation is Pi / 2 radians out of phase of the natural frequency of the spring mass system? I guess this makes the amplitude of the spring mass system to oscillate at a maximum amplitude.. Am I correct? Thanks in advanced..
 
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Victorian91 said:
What happens if the frequency of the forced oscillation is Pi / 2 radians out of phase of the natural frequency of the spring mass system? I guess this makes the amplitude of the spring mass system to oscillate at a maximum amplitude.. Am I correct? Thanks in advanced..

How can the frequencies be "out of phase"? Or in phase.
Frequency is a number, a quantity. It has no phase. Unless you mean some complex frequency, that includes dissipation.
Can you explain more?
 
I guess he tried to express the excitation as: F=cos(w*t-pi/2)
 
First of all I would like to apologize if I made myself unclear..

Anyway here it goes..
Basically, if we plot a graph of phase difference between the driving pendulum and driven pendulum against the frequency of the forced oscillation, at the natural frequency of the pendulum, the phase difference will be Pi / 2 radians. Is this correct?

I thought that if the driving pendulum and the driven pendulum is in phase it will have maximum amplitude..

I hope that my description now clears the air more.. Thanks a lot..
 

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