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Pendulums and circular tracks

Many amusement rides are basically pendulums, from traditional pirate ships to more recent additions of giant gyro swings. The pendulum has been a part of physics since Galileo discovered that the time for a full swing was independent of the amplitude of the swing (at least for small oscillations), but depends on the length of a pendulum:

The formula holds for a "mathematical pendulum", which is a point-like mass suspended from a massless swing. It is a surprisingly good approximation for also more realistic pendulums, as illustrated by the various objects suspended from different-length strings in one of the photos to the right and playgrounds swings. The article below discusses the Little Rockin Tug:

Other pendulum motions at Liseberg

(The links go to Swedish www-pages, that include data and some also accelerometer graphs)

Earlier pendulum rides at Liseberg:

Some of these reach large angles during the swing. Check the corrections for large angles and deviations from point particles on massless strings for a physical pendulum.

Other oscillations

  • The Wave swinger rides involves an oscillation due to the tilt of the roof. In this case, the period is modified by the accelerated motion around the carousel.
  • The gondolas in Mechanica swing back and forth.