The pendulum
The pendulum is a class of different settings in physics composed of an object whose dynamics is composed of gravity and the tension of a string.
Newtonian mechanics
Basic case
The basic example of a pendulum is given by the following approximations :
- The string itself has negligible mass
- The string is rigid (ie it is always of the same length)
- The Earth's gravitational field is a constant downward force
- There are no friction forces involved
With those approximations, the system describes a point mass subject to a constant downward force, along with a tension force in the direction of the central point in which the string is affixed. The constraint of the string always being of the same length means that, if the central point is at coordinates $0$, we have
\begin{equation} | \vec{x}(t) | = \ell \end{equation}