how to get googly eyes linked to object movement

Question

Now i have my muppet head moving up and down I'd like to get his googly eyes reacting to the head motion and settling when the motion stops. The pupils inside the eye 'dome' should randomly bounce around while the character is talking and then come to a stop at the bottom when the character stops talking. it should look like gravity is in play. I dont know if this should be linked to the head movement or the dialogue. I've found expresssions for sine waves, pendulums and wiggle but they dont quite achieve the effect. Any ideas much appreciated!

ShiveringCactus · Answer

Here's what I got with a little bit of playing:

I created a white circle for the eye, set to 100 pixels radius. Then I made a smaller black pupil and made it a child of the white circle and also used it as the track matte. Then I adapted Dan Ebberts' Elastic Expression, so that I could limit the range of movement:
https://www.motionscript.com/design-guide/elastic.html

restLength = 20;
damp = .99;
leader = thisComp.layer("Eye");

fDur = thisComp.frameDuration;
currFrame = Math.round(time / fDur);

p2 = position.valueAtTime(0);
v2 = 0;
for (f = 0; f <= currFrame; f++){
  t  = f*fDur;
  p1 = leader.transform.position.valueAtTime(t);
  delta = p2 - p1;
  nDelta = normalize(delta);
  a = 2 * nDelta * (length(delta) - restLength) * fDur;
  v2 = (v2 - a) * damp;
  p2 += v2;
}
p2
x = linear(p2[0],0,thisComp.width,-50,50);
y = linear(p2[1],0,thisComp.height,-50,50);
[x,y]

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