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Frequency is a fundamental concept that describes how often something happens within a particular period. Imagine you are listening to music. The beats per minute tell you how often those beats occur in that minute. Frequency, denoted by the letter \( f \), works similarly. It measures the number of complete oscillations, cycles, or repeating events, that occur in one second.
The unit of frequency is Hertz (Hz), where 1 Hz means one cycle per second. This can apply to waves like sound waves, light waves, or even the swings of a pendulum. So, if a wave has a frequency of 5 Hz, it completes 5 cycles every second. This makes frequency a handy measure for understanding the dynamics of different physical phenomena.

Angular frequency offers another way to look at how fast something is oscillating. Rather than using cycles per second, it considers how fast the wave moves in terms of angles.
Angular frequency is denoted by the Greek letter \(\omega\) (omega) and is measured in radians per second (rad/s). Radians are a way of measuring angles, where a complete circle is \(2\pi\) radians.
This form of frequency is often used in physics and engineering, where waves are not just concerned with the number of cycles, but how they move through their phase. This makes angular frequency extremely useful when discussing circular motions or periodic functions.

Oscillation is a term that represents motion repeated periodically. You can think of oscillation as the back and forth motion of something like a simple pendulum, a piano wire vibrating after being struck, or even the up and down motion of a seesaw.
Oscillations can vary in their speed and the time it takes to complete a full cycle is called the period. For example, if a pendulum swings back to its starting position in 2 seconds, that is its period.
Frequency comes into play here, as it defines how many of those oscillations happen in one second, giving a clearer picture of the oscillating motion.

When we talk about frequency, we measure it in Hertz, abbreviated as Hz. Named after the German physicist Heinrich Hertz, it is the unit of frequency in the International System of Units (SI).
One Hertz equals one cycle per second, making it an easy way to express how often something happens. For instance, if you have a fan that makes 60 rotations in a minute, its frequency is 1 Hz because it makes one complete rotation every second.
The use of Hertz makes it straightforward to compare different frequencies, whether you're dealing with light waves, radio signals, or anything else involving periodic movements.

Radians per second is a unit that specifically measures angular frequency. It combines the idea of radians, which measures angles, with time, measured in seconds.
Imagine a wheel spinning. If it rotates through one complete circle (\(2\pi\) radians) every second, its angular frequency is \(2\pi\) radians per second. This representation links the physical rotation to time, which is integral in understanding waves and oscillations.
By using radians per second, we can accurately describe rotating systems or waves and how rapidly they traverse their paths, making it a key concept in the analysis of periodic or circular motion.