A dynamic system for making use of an exercise bicycle supported on front and rear struts, the system permitting the bicycle to sway side to side when ridden vigorously, the system including a first and a second housing for resting on a support surface, a platform retained by each housing, the platform of the first housing serving to receive thereon the bicycle front strut and the platform of the second housing serving to receive thereon the bicycle rear strut, each platform being pivotal end to end and at least one deflectable resilient member engaging each platform and functioning to normally retain the exercise bicycle uprightly.