The period of harmonic oscillations of a material point, oscillating along the oX axis, T = 1.8 s. After what is the minimum time

The period of harmonic oscillations of a material point, oscillating along the oX axis, T = 1.8 s. After what is the minimum time interval for the point of passage from the extreme position to the middle of the amplitude?

It is convenient for us to describe the oscillations of a point by the harmonic function cos wt, because at the initial moment of time t = 0 it sets the extreme position (cos 0 ° = 1).
А = А₀ * cos wt.
Let us express the angular frequency in terms of the period:
w = 2pi / T
A = A₀ * cos ((2 * pi * t) / T)
By condition, the deviation is equal to half the amplitude:
A = 0.5A₀;
0.5А₀ = А₀ * cos ((2 * pi * t) / T)
cos ((2 * pi * t) / T) = 0.5
The minimum argument at which the function cos 2 * pi * t / T = 0.5 is pi / 6.
(2 * pi * t) / T = pi / 6;
2t / T = 1/6;
t = T / 12 = 1.8 s / 3 = 0.15 s.

Answer: 0.15 s.