Rroot locus

apwidth=800;
  apheight=600;
  Cream=[255,255,239];

var omega=0;
  var zeta=0;
  var zim=0;
  var angle=0;
  var zmod;

function circle(){
     Colour(Black);
     LineStart(1,0);
     for(i=0;i<6.283;i+=.05){
       LineTo(Math.cos(i),Math.sin(i));
     }
  }

InitGraph();
  ScaleWindow(-1.6,-1.2,1.6,1.2);
  DrawAxes();
  Colour(Black);
  circle();

for(angle=-Math.PI/2; angle<=Math.PI/2+.1;angle+=Math.PI/16){
    zeta=Math.cos(angle);
    zim=Math.sin(angle);
    zmod=Math.exp(-zeta*.25);
    LineStart(zmod*Math.cos(zim*.25),zmod*Math.sin(zim*.25));
    for(omega=.25;omega<=3.142;omega+=.05){
       zmod=Math.exp(-zeta*omega);
       LineTo(zmod*Math.cos(zim*omega),zmod*Math.sin(zim*omega));
    }
//    Label(Math.round(100*zeta)/100,-2.1*zeta-.1,2.1*zim);

}

for(omega=Math.PI/8;omega<=3.15;omega+=Math.PI/8){
    zeta=0;
    zim=-1;
    zmod=Math.exp(-zeta*omega);
    LineStart(zmod*Math.cos(zim*omega),zmod*Math.sin(zim*omega));
    for(angle=-Math.PI/2; angle<=Math.PI/2;angle+=.01){
      zeta=Math.cos(angle);
      zim=Math.sin(angle);
      zmod=Math.exp(-zeta*omega);
      LineTo(zmod*Math.cos(zim*omega),zmod*Math.sin(zim*omega));
    }
//    Label(omega,.1,omega);
  }