f[w_, w0_, 
        g_]  =  ((w^2  -  w0^2)^2  +  
            g^2 w^2)^(- .5)

Plot[f[w, 100, 100], {w, 0, 300}, PlotRange -> All]

FindMaximum[f[w, 100, 10], {w, 100}]

Maximize[f[w, 100, 10], w]

phi[w_, w0_, 
        g_]  =  -ArcTan[g  w/(w^2  -  w0^2)]

Plot[phi[w, 100, 10], {w, 0, 300}]