Fundamental Physics/Motion/Pendulum Oscillations

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Pendulum Oscillations[edit | edit source]

Animation of a pendulum showing the velocity and acceleration vectors.

A so-called "simple pendulum" is an idealization of a "real pendulum" but in an isolated system using the following assumptions:

  • The rod or cord on which the bob swings is massless, inextensible and always remains taut;
  • The bob is a point mass;
  • Motion occurs only in two dimensions, i.e. the bob does not trace an ellipse but an arc.
  • The motion does not lose energy to friction or air resistance.
  • The gravitational field is uniform.
  • The support does not move.

The differential equation which represents the motion of a simple pendulum is

 Eq. 1

where g is acceleration due to gravity, l is the length of the pendulum, and θ is the angular displacement.