page_title: Pendulum (mathematics)
section_title: Simple gravity pendulum
hierarchical_section_title: Pendulum (mathematics) / Simple gravity pendulum
context_page_description: A pendulum is a body suspended from a fixed support so that it swings freely back and forth under the influence of gravity. When a pendulum is displaced sideways from its resting, equilibrium position, it is subject to a restoring force due to gravity that will accelerate it back toward the equilibrium position. When released, the restoring force acting on the pendulum's mass causes it to oscillate about the equilibrium position, swinging it back and forth. The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allow the equations of motion to be solved analytically for small-angle oscillations.
context_section_description: A simple gravity pendulum is an idealized mathematical model of a real pendulum. This is a weight (or bob) on the end of a massless cord suspended from a pivot, without friction.  Since in this model there is no frictional energy loss, when given an initial displacement it will swing back and forth at a constant amplitude.  The model is based on these 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.
caption: Figure 1. Force diagram of a simple gravity pendulum.