The point performs harmonic oscillations with a period of 12 s.

The point performs harmonic oscillations with a period of 12 s. Determine how long it takes for the point to accelerate from zero to half the maximum value.

Let’s find the cyclical frequency of the point:
ω = 2π / T = 2π / 12 = π / 6 radians per second.
With harmonic vibrations, the acceleration of the body changes according to the law: a = Asin (ωt), where A is the maximum value, then:
a (t) = A / 2 = Asin (ωt)
sin (ωt) = 1/2
ωt = π / 6
t = π / 6: ω = π / 6: π / 6 = 1 s.