> Abstract. A jogger’s ponytail sways from side to side as the jogger runs, although her head
does not move from side to side. The jogger’s head just moves up and down, forcing the ponytail to
do so also. We show in two ways that this vertical motion is unstable to lateral perturbations. First
we treat the ponytail as a rigid pendulum, and then we treat it as a flexible string; in each case, it is
hanging from a support which is moving up and down periodically, and we solve the linear equation
for small lateral oscillation.