SIMPLIFIED: "16.2: Period and Frequency in Oscillations"

Link:  https://phys.libretexts.org/Bookshelves/College_Physics/College_Physics_1e_(OpenStax)/16%3A_Oscillatory_Motion_and_Waves/16.02%3A_Period_and_Frequency_in_Oscillations#:~:text=The%20time%20to%20complete%20one,which%20is%20by%20definition%20repetitive

Note: The above image was taken from the original article.

This article talks about the difference between frequency and period in oscillations. Before I can break down the difference or even define what frequency and period are, I think I should clarify what an oscillation is. An oscillation is a type of movement where there are repeated movements from a center position. That is probably a very confusing definition so here is an example: when you play with a pendulum, the ball that is attached on the string swings to one side, then swings to the other side while crossing the center/middle position, and then keeps on swinging back and forth while crossing the middle every time it swings. This is an example of oscillatory motion.

Now, period and frequency are two related but different ideas in oscillations. Here is the difference: period refers to how long ONE OSCILLATION TAKES. If we use the same pendulum example, the period would be however long it takes from the ball to swing from one side to the other, and then back to its original side. The unit of period is almost always in seconds. 

However, frequency is a different idea; frequency refers to how many oscillations occur in one second. The unit for frequency is called a hertz. Here is a quick example also with the pendulum: if the ball on the pendulum can swing back and forth 100 times in one second (this is very unrealistic but I’m just using 100 as an easy example), then the frequency of the oscillation would be 100 hertz. 

You might be thinking what the relationship is between the two variables. Here is the equation: Period = 1 divided by the Frequency. (Period = 1/Frequency). This means that if frequency increases, then the period decreases. Let’s try to verify this mathematically. If the frequency of oscillation increases for the pendulum example, for instance the frequency goes from 100 hertz to 200 hertz, then the period decreases, because it would take less time to finish one oscillation; the pendulum would be swinging twice as fast. Ultimately, period and frequency are inversely related, meaning if you increase one of them, the other one will decrease.