WOLFRAM|DEMONSTRATIONS PROJECT

Synchronizing Pendulum Clocks

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pendulum parameters
mass
1
1
ℓ
1
1
mass
2
1
ℓ
2
1
g
9.8
initial conditions
x
10
0
x
20
1
θ
10
-0.4
θ
20
0
clock parameters
λ
0.1
θ
0.2
interaction parameters
M
0.3
ρ
0.2
k
10
run animation
This simulation shows the anti-phase and the in-phase synchronization of two pendulum clocks. The interaction between the pendulums is mediated by a massless spring with stiffness constant
k
. The pendulums are attached to two masses with mass constant
M
, and
ρ
is the damping of the masses. The parameters
λ
and
θ
are associated with the limit cycle of the individual pendulum clocks. In some cases, the clocks always synchronize in anti-phase. In other cases, depending on the initial conditions, the clocks can synchronize with the same phase or in anti-phase.