The Near-Sighted Monkey

Dearest Unthinkable Mind students,

Here is something to stare at when you feel lost or uncertain about a drawing you are working on. I am in Santa Barbara and I am thinking about you all and missing our class.

Professor Old Skull

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.

  1. educarconlaciencia reblogged this from badsciencejokes
  2. anactualamphibian reblogged this from allofthemath
  3. w1ld-roses reblogged this from 1ucasvb
  4. kenji-nakamura reblogged this from 1ucasvb
  5. tarotconsulta reblogged this from rosaurajung
  6. demonputty reblogged this from spring-of-mathematics
  7. pedrinpapelin reblogged this from 1ucasvb
  8. tincalcetin reblogged this from 1ucasvb
  9. vicesofvincents reblogged this from 1ucasvb
  10. theridehomee reblogged this from 1ucasvb
  11. accessinfinity reblogged this from 1ucasvb
  12. gummalanavneeth reblogged this from 1ucasvb
  13. silverkitsune reblogged this from autumnlock
  14. autumnlock reblogged this from 1ucasvb
  15. derwolfsschanze reblogged this from notationnotes
  16. lovergrimmjow reblogged this from 1ucasvb
  17. iamnightmareindustries reblogged this from 2voyager
  18. waffletardage reblogged this from 1ucasvb
  19. pretty-maths reblogged this from 1ucasvb
  20. porterofmore reblogged this from pardonmyfingersastheysay and added:
    pardonmyfingersastheysay "eventually the pendulum swings, don’t forget america this how you made me"
  21. ghost-star reblogged this from the-hooded-figures
  22. soscialia reblogged this from zenarchism
  23. the-beat-goes-onn reblogged this from zenarchism
  24. zenarchism reblogged this from finally-trying-something-new