There may be merit in demonstrating the phugoid effect as part of Effects of Controls, but, as others have already said, under controlled conditions. The demo shows how the helicopter is dynamically unstable longitudinally. This should link into ground studies, but more importantly to the pilot's need make continual small control inputs to select and maintain an attitude. On aircraft where there is a stability augmentation system, these inputs are being made upstream of the stick position by the system.
I'm intrigued and a little worried at any suggestion that the cyclic should be let go of. Certainly NOT in the R22, nor in any other aircraft without a stick trim that will hold the cyclic.(And even then the hand should be hovering over the cyclic.) If there is no stick trim the demo can be achieved by freezing the cylcic position and observing the result. The whole point should be that the phugoid in a helicopter is divergent, and that each successive cycle will result in greater pitch attitudes. There is thus no need to pursue this, if you want to make the point, more than about one and a half cycles. More than that starts to worry me...and I've done this professionally as a test pilot.
Note that there will be cross-coupling effects of roll and yaw as well.
Given the R22's dislike for low-g manoeuvres, overall it's an exercise best avoided and certainly not one that should be prolonged.
[This message has been edited by Multp (edited 10 March 2001).]