Answer:
X = A sin ω t is the simplest equation for SH
V = ω A cos ω t describes the velocity where ω A is the maximum speed
cos ω t = 1/2 describes 1/2 the maximum speed
then ω t = 60 deg (cos 60 = 1/2)
X = A sin 60 will then be the displacement at 1/2 the maximum speed
or X = .866 A = 3^1/2 / 2 A
