Best answer:
T is the "period" of the motion -- the time it takes to complete one complete cycle. One complete cycle can be thought of as going around a circle once. There are 2π radians in a complete circle, so 2π/T is the "angular" (or "circular") frequency, commonly written as "ω". ...
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Best answer: T is the "period" of the motion -- the time it takes to complete one complete cycle. One complete cycle can be thought of as going around a circle once. There are 2π radians in a complete circle, so 2π/T is the "angular" (or "circular") frequency, commonly written as "ω". ω = 2π/T has units of 1/time. When multiplied by time, the quantity ω*t is unitless, as it must be if it's to be the argument of a trig function.
When t is some integral multiple of T, (i.e., n*T), the system has undergone n complete cycles. On the other hand, if, say, t = T/2, the system has only gone halfway through a cycle, and the argument of the cosine function becomes (2π/T)*(T/2) = π, or halfway around the circle (halfway through a cycle), etc..
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7 hours ago