Show that, if a system moves periodically, then the average of the total external force over a period of the motion must be zero.
A juggler juggles four balls of masses M, 2M, 3M and 4M in a periodic manner. Find the time average (over a period) of the total force he applies to the balls. The juggler wishes to cross a shaky bridge that cannot support the combined weight of the juggler and his balls. Would it help if he juggles his balls while he crosses?