3 pendulums problem

1. May 13, 2004

boeledi

HELP. I need to find a solution to the following problem.

3 totally independent pendulums oscillate with 3 distinct pulsations. There is no mention of any gravity, ... => the motion is infinite.

The 3 pendulums have the very same amplitude (A).

We then consider the following equation:

y = A sin(w t + phi)

Therefore, we obtain:

y1(t) = A sin(w1 t + phi1)
y2(t) = A sin(w2 t + phi2)
y3(t) = A sin(w3 t + phi3)

Question:

phi1, phi2, phi3 are the initial "positions" of the system at time t0 (it is a snapshot of the running system).

For each w : w1 < > w2 < > w3, at a certain moment of time t, we must have: y1(t) = y2(t) = y3(t)

How is it possible to obtain this time t <> t0 ?

Would there be any equation, statistical method, ... that might solve this problem ?