Coupled Pendulum Oscillations

initial angle rod 1,

θ

1

0

initial angle rod 2,

θ

2

0

mass 1,

m

1

1

mass 2,

m

2

1

rod length 1,

l

1

5

rod length 2,

l

2

5

spring stiffness k

1

release system

Two pendulums, connected by a massless spring, are allowed to vibrate in the same vertical plane. For the limiting case of small oscillations, the equations of motion for the system are given by

m

1

l

1

..

θ

1

+g

m

1

θ

1

+k(

l

1

θ

1

-

l

2

θ

2

)=0

,

m

2

l

2

..

θ

2

+g

m

2

θ

2

+k(

l

2

θ

2

-

l

1

θ

1

)=0

,

where

g

is the acceleration of gravity. You set the masses, lengths and initial displacements. The resulting graph shows the angle between the two pendulums as a function of time.