Time period and natural frequency

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Discussion Overview

The discussion revolves around the concepts of natural time period and natural frequency, particularly in the context of simple harmonic motion (SHM) and other periodic motions. Participants explore whether these terminologies are exclusive to SHM or applicable to other types of periodic motions.

Discussion Character

  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question whether the terms natural time period and frequency are limited to simple harmonic motions or if they can also apply to other periodic or sinusoidal motions.
  • There is a suggestion that natural frequency typically refers to the frequency of the fundamental mode.
  • One participant posits that the fundamental mode is always simple harmonic, raising the question of whether natural frequency and time period can be relevant for any periodic motion.
  • Another participant emphasizes that for a frequency or period to be considered "natural," there should be a clear reason for its preference over other frequencies, citing examples like the simple harmonic oscillator and vibrating strings, while contrasting this with the Earth's rotation, which lacks a compelling reason for its specific frequency.

Areas of Agreement / Disagreement

Participants express differing views on the applicability of natural frequency and time period to various types of periodic motions, indicating that the discussion remains unresolved with multiple competing perspectives.

Contextual Notes

Participants have not fully defined the terms being discussed, and there are unresolved assumptions regarding the criteria that make a frequency or period "natural." The discussion also touches on the distinction between fundamental modes and other periodic motions without reaching a consensus.

svishal03
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A fundamnetal question here;

IS it that the terminologies natural time period and frequency are used only for simple harmonic motions and not for motions which are periodic/sinusoidal like an SHM?
 
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svishal03 said:
A fundamnetal question here;

IS it that the terminologies natural time period and frequency are used only for simple harmonic motions and not for motions which are periodic/sinusoidal like an SHM?
Usually, natural frequency refers to the frequency of the fundamental mode.

http://hyperphysics.phy-astr.gsu.edu/hbase/sound/reson.html#c3
 
And when we say fundamental mode, it is always simple harmonic, right?

Am I right natural frequency and time period can be used for motions which have a periodicity?
 
Not just a periodicity but some clear reason why that frequency or period is more natural than any other. For example, the simple harmonic oscillator has a natural frequency which is determined by the ratio of spring constant to mass. Similarly a vibrating string has a fundamental frequency determined by the density, spring constant, and length.

The rotating Earth on the other hand is more or less periodic but there is no overwhelming reason why it wants to rotate at 1 cycle/day as opposed to any other frequency.
 

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