Period and Frequency
In simple oscillations, a particle completes a round trip in a certain period of
time. This time, T, which denotes the time it takes for an oscillating particle to return to its initial position, is called the period of oscillation. We also define another concept related to time, frequency. Frequency, denoted by ν, is defined as the number of cycles per unit time and is related to period as such:
Period, of course, is measured in seconds, while frequency is measured in
Hertz (or Hz), where 1 Hz = 1 cycle/second. Angular frequency defines
the number of radians per second in an oscillating system, and is denoted by
σ. This may seem confusing: most oscillations don't engage in circular
motion, and can't sweep out radians like in rotational motion. However,
oscillating systems do complete cycles, and if we think of each cycle as
containing
2Π radians, then we can define angular frequency. Again, angular
frequency for oscillations may seem a bit odd for now, but it will make more
sense when we compare oscillations and circular motion. For now, we can relate
our three variables dealing with the cycle of oscillation:
σ = 2Πν = 

Equipped with these variables, we can now look at the special case of the simple
harmonic oscillator.