Resonance: 90 degrees out of phase

 I set up coupled pendulums. I set one pendulum off. It wobbled the connecting string along the top which forced the second pendulum to move. Since they were the same length, the second pendulum was being forced at its natural frequency which meant that large amplitude oscillations were the result. The system is complicated in that the first pendulum transfers its energy to the second, so that the first one stops. Then the second pendulum transfers the energy back. There is a phase difference of pi/2 radians or 90 degrees between the driver and the driven. In the picture below you can make out one blurred pendulum level with the clamp stand in the middle of the oscillation and the other at amplitude on the right.