g=9.8;
l=0.3;
ContourPlot[ω^2/2-g/l Cos[θ],{θ,-3Pi,3Pi},{ω,-15,15},
Contours->{0,0.25g/l,0.5g/l,g/l,2g/l,3g/l,4g/l},
ContourShading->False,
Frame->False,
Axes->True,
Ticks->{Range[-4Pi,4Pi,Pi],Range[-20,20,10]}]