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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.
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