令wx=a
f（x）=sin²a+√3sinacosa=（1-cos2a）/2+√3/2sin2a
=1/2+√3/2sin2a-1/2cos2a
=sin（2a-π/6）+1/2
=sin（2wx-π/6）+1/2
根据题意
2π/2w=π
w=1