Fundamental Physics/Motion/Pendulum Oscillations
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
where g is acceleration due to gravity, l is the length of the pendulum, and θ is the angular displacement.