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

[raja.ganguly]

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 ?

 

[raja.ganguly]

Hey, I just figured out the answer... :)

 

[Chronos]

Looks like you are mixing frequency with amplitude.

 

[raja.ganguly]

No. wasn't mixing the two :p but I get what you mean and your logic. anyways, thanks :)

 

[PJC01]

The relationship between time and frequency in simple harmonic motion can be explained through the concept of periodic motion. In simple harmonic motion, the object oscillates back and forth in a regular and repeating pattern. This pattern is called a cycle or a period, denoted by T.

The frequency, denoted by f, is the number of cycles or periods that occur in one second. This means that for every second that passes, the object completes f cycles.

The formula T = 1/f simply represents the inverse relationship between period and frequency. This means that as the period increases, the frequency decreases, and vice versa.

In the example given, T = 10 seconds and f = 0.1 Hz, meaning that the object completes 0.1 cycles or periods in one second. This is equivalent to saying that it takes 10 seconds for the object to complete one cycle.

It is important to note that in simple harmonic motion, the distance covered by the object is not necessarily equal for each unit of time. As the object moves back and forth, it covers more distance in the middle of its oscillation and less distance at the ends. However, the time it takes for the object to complete one full oscillation remains constant, hence the relationship T = 1/f.

In summary, the formula T = 1/f in simple harmonic motion represents the inverse relationship between time and frequency, and it is a fundamental concept in understanding the behavior of objects undergoing this type of motion.