

For simplicity, this animation was made
using time periods of 16 and 18 time units. 
This is convenient because
9×16=(144)=8×18,
that is, the time time period of the "beats" is an integral number
of both the individual time periods. 

This is, of course, not necessarily the
case. 

For example we could
have used time periods of 10 units and 14 units but then we would
have had 
N×14=(N+1)×10 
which gives 
N=2.5 
This means that after 2.5 oscillations of
the lower frequency spring, the other spring would have completed
3.5 oscillations and the two would be in phase again. 

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