How to think of simple harmonic motion position equation?

I know the equation x(t) = Acos((2π/T)t) How does this work? I know cosθ. It repeats every 2π radians. I know a block's motion repeats every T radians. And amplitude A is something like scaling everything together. But why is x(t) = Acos((2π/T)t) ? How does putting (2π/T) make everything work? I can't... show more I know the equation

x(t) = Acos((2π/T)t)

How does this work?

I know cosθ. It repeats every 2π radians.
I know a block's motion repeats every T radians.
And amplitude A is something like scaling everything together.

But why is

x(t) = Acos((2π/T)t) ? How does putting (2π/T) make everything work? I can't wrap my mind around 2π/T. What is going on?
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