Synchronizing Pendulum Clocks

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.