"The mathematics of pendulums are in general quite complicated. Simplifying assumptions can be made, which in the case of a simple pendulum allows the equations of motion to be solved analytically for small-angle 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." [Pendulum (mathematics). Wikipedia]
The diagram example "Mathematical pendulum" was created using the ConceptDraw PRO diagramming and vector drawing software extended with the Physics solution from the Science and Education area of ConceptDraw Solution Park.