<< Graphics`Graphics`

ex. 8.4     Fig 8.10     p.183

unknown

para = {m -> 1, ϵ -> 1, θ -> 
          45  °, z ->  0.1}

balancing start

gg =  w^2/m/(s^2 + 2 z wn s + wn^2) /. s -> I w /. 
        w ->   p wn

tabp = {0.1, 0.3, 0.8, 0.9, 0.95, 1, 1.05, 1.1, 1.5, 2, 3}; 
    ne = Length[tabp]

polar[gw_, 
        iro_] := {pp = 
          Table[{Re[gw], -Im[gw], p} /. p ->  tabp[[i]], {i, 
              ne}]; DisplayTogether[
          ParametricPlot[{Re[gw], -Im[gw]}, {p, 0, 3}, 
            AspectRatio -> Automatic, PlotStyle ->  Hue[iro], 
            PlotRange ->  {{-5, 5}, {-5, 5}} ], 
          LabeledListPlot[pp]]}

step 1

gw1 = 
        Simplify[
          m ϵ Exp[I θ] gg /. para];

zu1 = polar[gw1, 0.9]

step 2

parat = {mtr ->  0.5, θt ->  
          180  °}

gw2 = 
        Simplify[(m ϵ Exp[I θ] + 
                    mtr Exp[I θt]) gg /. para /. 
            parat];

zu2 = polar[gw2, 0.7]

Show[zu1, zu2]

step 3

gw3 = 
        Simplify[(m ϵ Exp[I θ] + 
                    1.8 mtr Exp[I θt] Exp[I 45  °]) gg /. 
              para /. parat];

zu3 = polar[gw3, 0.5]

Show[zu1, zu2, zu3]

Plot[{Abs[gw1], Abs[gw2], Abs[gw3]}, {p, 0, 3}, 
      GridLines ->  Automatic, 
      PlotStyle ->  {Hue[0.9], Hue[0.7], Hue[0.5]}]