Maybe using Newton4 script or if you are familiar with expressions take a look at Bounce Expressions created by Dan Ebberts.
I made this simple walking rope animation using 3 expressions and 2 sliders. However, if you need to make the object fall, you'll likely have to edit all the expressions. It might be better to create your animation using keyframes and use a bounce expression to animate the rope while the object is falling.
BALL Layer
- anchor point expression:
// anchorPoint bottom center
a = sourceRectAtTime();
height = a.height;
width = a.width;
top = a.top;
left = a.left;
x = left + width/2;
y = top + height;
[x,y];
- Position expression:
// pathFollow
duration = thisComp.layer("LINE").effect("DURATION")(1);
linePath = thisComp.layer("LINE").content("Path 1").path;
linePath.pointOnPath (linear(time,0,duration,0,1), t=time)
LINE Layer
- Path expression:
// path
duration = effect("DURATION")(1);
lineWidth = 1000;
start = [thisComp.width/2 - lineWidth/2, thisComp.height/2];
end = [thisComp.width/2 + lineWidth/2, thisComp.height/2];
ball = thisComp.layer("BALL").position;
weight = effect("WEIGHT")(1);
middle= linear(time,0,duration,start,end);
middleY = time<duration?middle[1] + Math.sin(time/Math.PI) * weight:thisComp.height/2;
createPath([start,[middle[0],middleY],end],[[0,0],[-middleY + thisComp.height/2,0],[0,0]],[[0,0],[middleY - thisComp.height/2,0],[0,0]],false)
And 2 sliders control (WEIGHT and DURATION on LINE Layer.