A double pendulum is coupled with a spring.  Two modes of vibration with different frequencies are possible.  One has the pendula swinging in opposite directions, alternately compressing and expanding the connecting spring.  The second mode has the pendula swinging in the same direction, and the spring does not change length at all.

Start with the pendula at rest.  Move the pendula equally toward each other, compressing the spring.  Release the system and use a timer to find the period.

Again, start from rest and move the pendula an identical amount in the same direction.  Release them and find the period. The pendula should move together, not changing the length of the spring.

Calculate the frequencies of the two modes of oscillation of the system.