Different modes of oscillation for a pendulum
The period of a simple pendulum is not a trivial thing, and it depends on the initial conditions.
Shown here are ten different modes of oscillation for the same pendulum. The only difference is the total amount of mechanical energy in the system.
As a result, each one has a completely different period of oscillation, unlike what the small-angle approximation (as taught in high-school) would suggest. They can’t be in sync. You may see some really interesting patterns based on the delay between them in your browser.
The red graph above each pendulum represents the phase portrait for the respective mode of oscillation, with the current state marked as a blue dot. The horizontal axis represents angle (hence why it wraps around the sides) while the vertical axis represents angular velocity.
Pendulums are very interesting dynamical systems, as they are relatively simple to understand but can produce surprisingly complex results in certain cases, such as the chaotic behavior of double pendulums and the odd behavior displayed by coupled pendulums.
Marina Abramovic - Rhythm 10 (1973)
“In her first performance Abramovic explored elements of ritual and gesture. Making use of twenty knives and two tape recorders, the artist played the Russian game in which rhythmic knife jabs are aimed between the splayed fingers of her hand. Each time she cut herself, she would pick up a new knife from the row of twenty she had set up, and record the operation.
After cutting herself twenty times, she replayed the tape, listened to the sounds, and tried to repeat the same movements, attempting to replicate the mistakes, merging past and present. She set out to explore the physical and mental limitations of the body – the pain and the sounds of the stabbing, the double sounds from the history and from the replication.
With this piece, Abramovic began to consider the state of consciousness of the performer. ‘Once you enter into the performance state you can push your body to do things you absolutely could never normally do.’”