Why is T = 1/f in Simple Harmonic Motion?

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Discussion Overview

The discussion revolves around the relationship between the period (T) and frequency (f) in simple harmonic motion (SHM), specifically questioning the interpretation of these concepts and their implications on motion characteristics.

Discussion Character

  • Debate/contested

Main Points Raised

  • One participant explains that in SHM, varying acceleration leads to different distances covered over time, using an example where T = 10s results in f = 0.1 Hz, and questions the interpretation of frequency in relation to distance covered.
  • Another participant suggests that there is a misunderstanding between frequency and amplitude, implying a potential confusion in the original claim.
  • A later reply indicates that the initial participant does not believe they are mixing frequency with amplitude, acknowledging the feedback while maintaining their perspective.

Areas of Agreement / Disagreement

Participants do not appear to reach a consensus, as there are differing interpretations of the relationship between frequency and amplitude, and the discussion remains unresolved.

Contextual Notes

The discussion includes assumptions about the definitions of frequency and amplitude, and the implications of varying acceleration in SHM, which are not fully explored or clarified.

raja.ganguly
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An object undergoing simple harmonic motion will always have varying acceleration. That means for each unit of time passing by, different distances will be covered within the bounded amplitude. As an example suppose T= 10s. Therefore, f = 1/T = 0.1 Hz(1/10th of a wavelength). This in a way would be like using the unitary method as-
If time taken for 1 complete oscillation is 10 seconds, then,
Time taken for 1/ 10 oscillation will be 1 second. (Modifying frequency's definition)

which cannot be, since thinking of it in that way would mean the body is covering equal distances of 1/10th of an oscillation every second till one time period of 1 second.

How is this all to be correctly explained ?
 
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Hey, I just figured out the answer... :)
 
Looks like you are mixing frequency with amplitude.
 
No. wasn't mixing the two :p but I get what you mean and your logic. anyways, thanks :)
 

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