The Problem of the Swing

The fact that a mechanical system so well known to so many in its practical aspect as the swing has been thoroughly neglected in textbooks and problem papers may justify a few remarks on it here. The only reference to the swing which I have been able to find is the question requiring it to be shown that the amplitude of the swing may be increased by internal action only, if, when the swing passes through its lowest position, the distance of the centre of gravity from the point of suspension is (suddenly) shortened from l to ( l – h ), the full distance l being restored at the end of the swing.