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1. Angular Frequency

   Linked via "radians"

   Definition and Basic Formulation
   In the most fundamental sense, angular frequency relates the period ($T$)) of a repeating event to the rate at which that event progresses in terms of radians per unit time. For a mechanical oscillator undergoing Simple Harmonic Motion (SHM) with a period $T$ measured in seconds, the angular frequency is defined as:
   $$\omega = \frac{2\pi}{T}$$

2. Angular Frequency

   Linked via "radians"

   $$\omega = \frac{2\pi}{T}$$
   This definition establishes the proportionality constant between linear frequency ($f$, measured in Hertz, where $f = 1/T$) and angular frequency. The factor of $2\pi$ arises because one complete cycle) corresponds to a phase change of $2\pi$ radians [2].
   Relationship to Velocity