# Pendulums

There are a number of different forms of pendulum. The main characteristic being that when the mass is displaced from it's position of rest it will oscillate at a fixed frequency.

 Simple Pendulum As used in the simplest mechanical clock designs. where τ = period [s] l = length [m] g = gravitational acceleration [ms-2]
 Conical Pendulum Note that it would be necessary to throw the bob into a circular motion to start it and then once settled the equation may be applied. where τ = period [s] l = length [m] α = cone half-angle [rad] g = gravitational acceleration [ms-2]
 Torsional Pendulum Another simple design used in some types of clock. where τ = period [s] l = length [m] I0 = moment of inertia of bob [kgm2] kt = torsional rigidity [Nm2]

### Historical Notes

1. 1581 Galileo uses his pulse to time the swinging of the lamps in the cathedral at Pisa. He concludes that the time for a lamp to swing does not depend on the angle through which it swings. This observation eventually leads to the development of pendulum clocks.