(1)
f(x)=sinωx+2√3sin²ωx/2
=sinwx+√3(1-coswx)
=sinwx-√3coswx+√3
=2(1/2sinwx-√3/2coswx)+√3
=2sin(wx-π/3)+√3
∵f(x)最小正周期为2π/3
∴2π/w=2π/3
∴w=3
∴f(x)=2sin(3x-π/3)+√3
(2)
f(x)的图像向左平移π/2个单位,
得g(x)=2sin[3(x+π/2)-π/3]+√3的图像
∴g(x)=2sin(3x+7π/6)+√3
g(x)≥2√3
即2sin(3x+7π/6)+√3≥2√3
∴sin(3x+7π/6)≥√3/2
∴2kπ+π/3≤3x+7π/6≤2kπ+2π/3,k∈Z
∴2kπ-5π/6≤3x≤2kπ-π/2,k∈Z
∴2kπ/3-5π/18≤x≤2kπ/3-π/6,k∈Z
∴g(x)≥2√3的解集为
｛x|2kπ/3-5π/18≤x≤2kπ/3-π/6,k∈Z}