  In this paper we study the system of two falling balls in continuous time. We
modell the system by a suspension flow over a two dimensional, hyperbolic base
map. By detailed analysis of the geometry of the system we identify special
periodic points and show that the ratio of certain periods in continuous time
is Diophantine for almost every value of the mass parameter in an interval.
Using results of Melbourne (\cite{M}) and our previous achievements \cite{BBNV}
we conclude that for these values of the parameter the flow mixes faster than
any polynomial. Even though the calculations are presented for the specific
physical system, the method is quite general and can be applied to other
suspension flows, too.
