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For simplicity, this animation was made using time periods of 16 and 18 time units.
This is convenient because 916=(144)=818, 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
N14=(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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