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

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In simple harmonic motion, the relationship T = 1/f indicates that the period (T) is the inverse of frequency (f). An object in this motion experiences varying acceleration, leading to different distances covered over time within its amplitude. For example, if T is 10 seconds, the frequency f is 0.1 Hz, meaning one complete oscillation occurs every 10 seconds. Misunderstanding this relationship can lead to incorrect assumptions about equal distances covered in fractional oscillations. The discussion clarifies that frequency and amplitude are distinct concepts, emphasizing the importance of accurately interpreting their definitions.
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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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