Question

In harmonic motion, why when the books describe the angular frequency, they assumes x(t) (motion equation) as equal to x(t+T) (T as the period), i just cant understand why x(t) = x(t+T).

(sorry if i am being confunsing in my explanation)

Answer 1

That's the definition of T - the time it takes to undergo one full cycle and come back to exactly where it started.