It may appear as if the helicopter reacts on a pendulum, but that is really due to pilot-induced oscillations.
+1 !
In fact that's exactly what Helofan says :
For example: from a hover - if you push forward on the cyclic till the aircraft begins to move forward then neutralise the cyclic, the helo will pitch down, move forward then level then would slightly nose up.
IF you then moved the cyclic back then neutralise the cyclic , the aircraft will pitch nose up, move back and then begin to move back.
The conclusion is then wrong (in my opinion) :
This swinging action ( pendular action ) is basically demonstrating the forces in place because the AC is suspended from a point & is free to move like so.
The AC isn't "free to move", it just responds to the pilot's inputs on the controls.
Its stability in a hover may be questioned but nothing more...