The inclusion of ##2π/T## in the equation for simple harmonic oscillators, represented as ##x(t) = Acos(2πt/T)##, is essential because the argument of the cosine function must be dimensionless. The term ##t/T## indicates the fraction of the oscillation period, T, that has elapsed, while ##2π## accounts for the total radians in a complete cycle. This formulation ensures that the argument of the cosine function accurately reflects the oscillatory nature of the motion.
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A simple answer is that there are 2π radians in a circle and t/T represents a fraction of a complete cycle. The wave repeats every T (the period). Then what @Doc Al said.Kaushik said:Summary:: ##x(t) = Acos(2πt/T)##
Why do we include 2π/T